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 A263401 Expansion of Product_{k>=1} (1 + x^k - x^(2*k)). 13
 1, 1, 0, 2, 0, 1, 3, 1, 1, 2, 6, 1, 4, 2, 5, 10, 5, 4, 9, 7, 8, 21, 9, 13, 13, 19, 13, 27, 32, 23, 29, 33, 27, 45, 37, 45, 79, 49, 57, 68, 82, 67, 101, 83, 109, 155, 124, 113, 174, 148, 171, 196, 215, 198, 262, 310, 269, 330, 314, 342, 414, 430, 393, 536, 493 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..5000 FORMULA a(n) ~ sqrt(log(phi)) * phi^sqrt(8*n) / (2^(3/4)*sqrt(Pi)*n^(3/4)), where phi = A001622 = (1+sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jan 03 2016 MATHEMATICA nmax = 80; CoefficientList[Series[Product[1+x^k-x^(2*k), {k, 1, nmax}], {x, 0, nmax}], x] nmax = 100; p = ConstantArray[0, nmax + 1]; p[[1]] = 1; p[[2]] = 1; p[[3]] = -1; Do[Do[p[[j+1]] = p[[j+1]] + p[[j - k + 1]] - If[j < 2*k, 0, p[[j - 2*k + 1]]], {j, nmax, k, -1}]; , {k, 2, nmax}]; p (* Vaclav Kotesovec, May 10 2018 *) CROSSREFS Cf. A000726, A002390, A055922, A100847, A109389, A162891, A266686. Sequence in context: A291316 A130504 A044942 * A239928 A114912 A231723 Adjacent sequences:  A263398 A263399 A263400 * A263402 A263403 A263404 KEYWORD nonn AUTHOR Vaclav Kotesovec, Jan 03 2016 STATUS approved

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Last modified September 17 12:40 EDT 2021. Contains 347477 sequences. (Running on oeis4.)