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 A035451 Number of partitions of n into parts congruent to 1 mod 4. 14
 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 4, 4, 4, 5, 6, 7, 7, 8, 10, 11, 12, 13, 15, 17, 18, 20, 23, 26, 28, 30, 34, 38, 41, 44, 49, 55, 60, 64, 70, 78, 85, 91, 99, 109, 119, 128, 138, 151, 164, 176, 190, 207, 225, 241, 259, 281, 304, 326, 349, 377, 408, 437, 467, 503, 542, 581 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,6 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 FORMULA G.f.: 1/prod(k>=0, 1-x^(4*k+1)). - Vladeta Jovovic, Nov 22 2002 G.f.: sum(n>=0, x^n / prod(k=1..n, 1-x^(4*k) ) ). [Joerg Arndt, Apr 07 2011] G.f.: 1 + sum(n>=0, x^(4*n+1) / prod(k>=n, 1-x^(4*k+1) ) ) = 1 + sum(n>=0, x^(4*n+1) / prod(k=0..n, 1-x^(4*k+1) ) ). [Joerg Arndt, Apr 08 2011] a(n) ~ Gamma(1/4) * exp(Pi*sqrt(n/6)) / (2^(19/8) * 3^(1/8) * n^(5/8) * Pi^(3/4)) * (1 + (Pi/(96*sqrt(6)) - 5*sqrt(3/2)/(16*Pi)) / sqrt(n)). - Vaclav Kotesovec, Feb 26 2015, extended Jan 24 2017 a(n) = (1/n)*Sum_{k=1..n} A050449(k)*a(n-k), a(0) = 1. - Seiichi Manyama, Mar 20 2017 MATHEMATICA nmax=100; CoefficientList[Series[Product[1/(1-x^(4*k+1)), {k, 0, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Feb 26 2015 *) CROSSREFS Cf. A035462, A035382, A050449. Cf. similar sequences of number of partitions of n into parts congruent to 1 mod m: A000009 (m=2), A035382 (m=3), this sequence (m=4), A109697 (m=5), A109701 (m=6), A109703 (m=7), A277090 (m=8). Sequence in context: A001156 A199119 A321423 * A304633 A124746 A124789 Adjacent sequences:  A035448 A035449 A035450 * A035452 A035453 A035454 KEYWORD nonn AUTHOR EXTENSIONS Offset changed by N. J. A. Sloane, Apr 11 2010 STATUS approved

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Last modified April 24 22:26 EDT 2019. Contains 322446 sequences. (Running on oeis4.)