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 A035386 Number of partitions of n into parts congruent to 2 mod 3. 14
 1, 0, 1, 0, 1, 1, 1, 1, 2, 1, 3, 2, 3, 3, 4, 4, 6, 5, 7, 7, 9, 9, 12, 11, 15, 15, 18, 19, 23, 23, 29, 29, 35, 37, 43, 45, 53, 55, 64, 68, 78, 82, 95, 99, 114, 121, 136, 145, 164, 173, 196, 208, 232, 248, 276, 294, 328, 349, 386, 413, 456, 486, 537, 572, 629, 673, 737, 787 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,9 COMMENTS a(n) = A116376(3*n). - Reinhard Zumkeller, Feb 15 2006 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 James Mc Laughlin, Andrew V. Sills, Peter Zimmer, Rogers-Ramanujan-Slater Type Identities , arXiv:1901.00946 [math.NT] FORMULA a(n) = 1/n*Sum_{k=1..n} A078182(k)*a(n-k), a(0) = 1. - Vladeta Jovovic, Nov 21 2002 Euler transform of period 3 sequence [ 0, 1, 0, ...]. - Michael Somos, Jul 24 2007 a(n) ~ Gamma(2/3) * exp(sqrt(2*n)*Pi/3) / (2^(11/6) * sqrt(3) * Pi^(1/3) * n^(5/6)) * (1 + (Pi/72 - 5/(3*Pi)) / sqrt(2*n)). - Vaclav Kotesovec, Feb 26 2015, extended Jan 24 2017 G.f.: A(x) = Sum_{n >= 0} x^(n*(3*n-1))/Product_{k = 1..n} ((1 - x^(3*k)) *(1 - x^(3*k-1))). (Set z = x^2 and q = x^3 in McLaughlin et al., Section 1.3, Entry 7.) - Peter Bala, Feb 02 2021 MAPLE g:=add(x^(n*(3*n-1))/mul((1-x^(3*k))*(1-x^(3*k-1)), k = 1..n), n = 0..6): gser:=series(g, x, 101): seq(coeff(gser, x, n), n = 0..100); # Peter Bala, Feb 02 2021 MATHEMATICA nmax=100; CoefficientList[Series[Product[1/(1-x^(3*k+2)), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 26 2015 *) nmax = 100; poly = ConstantArray[0, nmax + 1]; poly[[1]] = 1; poly[[2]] = 0; Do[If[Mod[k, 3] == 2, Do[poly[[j + 1]] -= poly[[j - k + 1]], {j, nmax, k, -1}]; ], {k, 2, nmax}]; poly2 = Take[poly, {2, nmax + 1}]; poly3 = 1 + Sum[poly2[[n]]*x^n, {n, 1, Length[poly2]}]; CoefficientList[Series[1/poly3, {x, 0, Length[poly2]}], x] (* Vaclav Kotesovec, Jan 13 2017 *) nmax = 50; s = Range[0, nmax/3]*3 + 2; Table[Count[IntegerPartitions@n, x_ /; SubsetQ[s, x]], {n, 0, nmax}] (* Robert Price, Aug 05 2020 *) PROG (PARI) {a(n)= if( n<0, 0, polcoeff( 1 / prod( k=1, n, 1 - (k%3==2) * x^k, 1 + x * O(x^n)), n))} /* Michael Somos, Jul 24 2007 */ CROSSREFS Cf. A035382, A035451, A262928. Sequence in context: A051274 A267806 A025797 * A244327 A319318 A029164 Adjacent sequences: A035383 A035384 A035385 * A035387 A035388 A035389 KEYWORD nonn,easy AUTHOR Olivier Gérard STATUS approved

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Last modified June 8 10:34 EDT 2023. Contains 363163 sequences. (Running on oeis4.)