A035974 - OEIS

A035974

Number of partitions of n into parts not of the form 19k, 19k+5 or 19k-5. Also number of partitions with at most 4 parts of size 1 and differences between parts at distance 8 are greater than 1.

1, 2, 3, 5, 6, 10, 13, 19, 25, 35, 45, 62, 79, 104, 133, 173, 217, 279, 348, 440, 546, 683, 840, 1043, 1275, 1567, 1907, 2328, 2815, 3416, 4111, 4957, 5940, 7125, 8498, 10148, 12055, 14327, 16959, 20075, 23673, 27920, 32816, 38562, 45185, 52923

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OFFSET

1,2

COMMENTS

Case k=9,i=5 of Gordon Theorem.

REFERENCES

G. E. Andrews, The Theory of Partitions, Addison-Wesley, 1976, p. 109.

LINKS

Table of n, a(n) for n=1..46.

FORMULA

a(n) ~ exp(4*Pi*sqrt(2*n/57)) * 2^(3/4) * cos(9*Pi/38) / (3^(1/4) * 19^(3/4) * n^(3/4)). - Vaclav Kotesovec, May 10 2018

MATHEMATICA

nmax = 60; Rest[CoefficientList[Series[Product[(1 - x^(19*k))*(1 - x^(19*k+ 5-19))*(1 - x^(19*k- 5))/(1 - x^k), {k, 1, nmax}], {x, 0, nmax}], x]] (* Vaclav Kotesovec, May 10 2018 *)

CROSSREFS

Sequence in context: A035959 A036801 A035966 * A035983 A035993 A036004

Adjacent sequences: A035971 A035972 A035973 * A035975 A035976 A035977

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved