Heritable epigenetic effects due to nutrition seem well established - you are what your mother and grandmother ate - but it may also be that you are what your mother played when she was a child.

. . . in young mice, brief exposure to a stimulating environment — including new toys and opportunities for exercise and social interaction — enhanced long-term potentiation (LTP), which is thought to form the cellular basis of memory.

In the current study, Feig and his colleagues found that the offspring of mothers who had experienced environmental enrichment before adolescence also showed enhanced LTP, despite never experiencing the stimulating environment themselves. . .

Just as environmental enrichment enhanced memory at the cellular level, it also enhanced memory at the behavioral level. . .

"A striking feature of this study is that enrichment took place during pre-adolescence, months before the mice were even fertile, yet the effect reached into the next generation," said senior author Feig.

"This study and others are revolutionizing our understanding of how nature — starting with an individual's DNA sequence — and nurture — including the way life experience alters the way DNA is expressed — can combine, not only to regulate the health of subsequent generations, but also possibly the incidence of disease,"

It's a mouse study, which does not prove that these effects are valid in humans, but it often so. I would proceed on the assumption that it is wise to provide a stimulating environment for your children. But there's a catch.

The researchers studied the brain function of pre-adolescent mice with a genetically-created defect in memory. When these young mice were enriched by exposure to a stimulating environment – including novel objects, opportunities for social interaction and voluntary exercise – for two weeks, the memory defect was reversed. The work showed that this enhancement was remarkably long-lasting because it was passed on to the offspring even though the offspring had the same genetic mutation and were never exposed to an enriched environment. . .

"The effect lasted until adolescence, when it waned, suggesting that this process is designed specifically to aid the young brain" . . .

So, it seems that each generation will need LTP, though I wonder if there is a compound effect?

"This example of 'inheritance of acquired characters,' was first proposed by Lamarck in the early 1800s. However, it is incompatible with classical Mendelian genetics, which states that we inherit qualities from our parents through specific DNA sequences they inherited from their parents. We now refer to this type of inheritance as epigenetics, which involves environmentally-induced changes in the structure of DNA and the chromosomes in which DNA resides that are passed on to offspring,"

It seems to be more than DNA that is affected. Other studies have noted RNA effects too. See Hybrid Dysgenesis which discusses the effects of piRNAs that are in egg cells, but not DNA, and that affect the expression of DNA. This means that some traits can be transmitted by daughters but not sons.