A025777 Expansion of 1/((1-x)*(1-x^5)*(1-x^7)).

1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 6, 7, 7, 8, 8, 9, 10, 11, 12, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 31, 32, 34, 35, 36, 38, 39, 41, 42, 44, 46, 47, 49, 50, 52, 54, 56, 58, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 84

Offset

0,6

References

L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 120, D(n;1,5,7).

Links

Table of n, a(n) for n=0..70.

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,-1,1,-1,0,0,0,-1,1).

Formula

a(n) = round((n^2+13*n+36)/70).

a(n) = a(n-1) + a(n-5) - a(n-6) + a(n-7) - a(n-8) - a(n-12) + a(n-13). - R. J. Mathar, Aug 21 2014

Mathematica

CoefficientList[Series[1/((1-x)(1-x^5)(1-x^7)), {x, 0, 60}], x] (* or *) LinearRecurrence[{1, 0, 0, 0, 1, -1, 1, -1, 0, 0, 0, -1, 1}, {1, 1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5}, 70] (* Harvey P. Dale, Apr 30 2018 *)

Prog

(PARI) Vec(1/((1-x)*(1-x^5)*(1-x^7)) + O(x^70)) \\ Jinyuan Wang, Feb 28 2020

Crossrefs

Sequence in context: A308358 A229803 A029123 * A269862 A194200 A242736

Adjacent sequences: A025774 A025775 A025776 * A025778 A025779 A025780

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Jinyuan Wang, Feb 28 2020

Status

approved