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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 * A093875 A266193 A114214

Adjacent sequences:  A116455 A116456 A116457 * A116459 A116460 A116461

KEYWORD

nonn

AUTHOR

Emeric Deutsch, Feb 16 2006

STATUS

approved

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Last modified October 13 18:14 EDT 2019. Contains 327981 sequences. (Running on oeis4.)