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 A116458 Number of partitions of n into parts congruent to 1, 9, or 11 (mod 14). 0
 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 6, 6, 7, 8, 9, 10, 11, 12, 12, 14, 15, 16, 17, 19, 21, 22, 24, 26, 29, 31, 34, 36, 38, 41, 44, 48, 51, 55, 60, 64, 68, 73, 79, 84, 91, 97, 103, 110, 117, 125, 133, 142, 152, 163, 172, 183, 196, 208, 222, 236, 250, 265, 281 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,10 COMMENTS Also number of partitions of n into distinct parts congruent to 1,2, or 4 (mod 7). Example: a(15)=4 because we have [15],[11,4],[9,4,2] and [8,4,2,1]. REFERENCES G. E. Andrews, Number Theory, Dover Publications, 1994 (p. 166, Exercise 7). LINKS Table of n, a(n) for n=0..72. FORMULA G.f.=1/product((1-x^(1+14j))(1-x^(9+14j))(1-x^(11+14j)),j=0..infinity). G.f.=product((1+x^(1+7j))(1+x^(2+7j))(1+x^(4+7j)),j=0..infinity). a(n) ~ exp(sqrt(n/7)*Pi) / (2*7^(1/4)*n^(3/4)). - Vaclav Kotesovec, Mar 07 2016 EXAMPLE a(15)=4 because we have [15],[11,1,1,1,1],[9,1,1,1,1,1,1] and [1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]. MAPLE g:=product((1+x^(1+7*j))*(1+x^(2+7*j))*(1+x^(4+7*j)), j=0..15): gser:=series(g, x=0, 95): seq(coeff(gser, x, n), n=0..77); MATHEMATICA nmax = 100; CoefficientList[Series[Product[(1+x^(7*k-6))*(1+x^(7*k-5))*(1+x^(7*k-3)), {k, 1, nmax}], {x, 0, nmax}], x] (* Vaclav Kotesovec, Mar 07 2016 *) CROSSREFS Sequence in context: A189631 A101402 A156251 * A354166 A331854 A093875 Adjacent sequences: A116455 A116456 A116457 * A116459 A116460 A116461 KEYWORD nonn AUTHOR Emeric Deutsch, Feb 16 2006 STATUS approved

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Last modified April 15 05:45 EDT 2024. Contains 371667 sequences. (Running on oeis4.)