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 A109697 Number of partitions of n into parts each equal to 1 mod 5. 10
 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 4, 4, 4, 4, 5, 6, 7, 7, 7, 8, 10, 11, 12, 12, 13, 15, 17, 18, 19, 20, 23, 26, 28, 29, 31, 34, 38, 41, 43, 45, 50, 55, 60, 63, 66, 71, 79, 85, 90, 94, 101, 110, 120, 127, 133, 141, 153, 165, 176, 184, 195, 210, 227, 241, 254, 267, 286, 307, 327 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 FORMULA G.f.: 1/product(1-x^(1+5j), j=0..infinity). - Emeric Deutsch, Mar 30 2006 a(n) ~ Gamma(1/5) * exp(Pi*sqrt(2*n/15)) / (2^(8/5) * 3^(1/10) * 5^(2/5) * Pi^(4/5) * n^(3/5)) * (1 - (3*sqrt(3/10)/(5*Pi) + Pi/(120*sqrt(30))) / sqrt(n)). - Vaclav Kotesovec, Feb 27 2015, extended Jan 24 2017 a(n) = (1/n)*Sum_{k=1..n} A284097(k)*a(n-k), a(0) = 1. - Seiichi Manyama, Mar 20 2017 EXAMPLE a(11)=3 since 11 = 11 = 6+1+1+1+1+1 = 1+1+1+1+1+1+1+1+1+1+1 MAPLE g:=1/product(1-x^(1+5*j), j=0..25): gser:=series(g, x=0, 85): seq(coeff(gser, x, n), n=0..80); # Emeric Deutsch, Mar 30 2006 MATHEMATICA Table[Count[IntegerPartitions[n], _?(Union[Mod[#, 5]]=={1}&)], {n, 0, 75}] (* Harvey P. Dale, Oct 08 2011 *) CROSSREFS Cf. A000041, A003105, A284097. Cf. similar sequences of number of partitions of n into parts congruent to 1 mod m: A000009 (m=2), A035382 (m=3), A035451 (m=4), this sequence (m=5), A109701 (m=6), A109703 (m=7), A277090 (m=8). Sequence in context: A025783 A025780 A199121 * A103373 A038539 A275891 Adjacent sequences:  A109694 A109695 A109696 * A109698 A109699 A109700 KEYWORD nonn AUTHOR Erich Friedman, Aug 07 2005 EXTENSIONS More terms from Emeric Deutsch, Mar 30 2006 STATUS approved

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Last modified October 17 07:05 EDT 2018. Contains 316276 sequences. (Running on oeis4.)