A025776 - OEIS

A025776

Expansion of 1/((1-x)*(1-x^5)*(1-x^6)).

1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 4, 5, 6, 6, 6, 7, 8, 9, 10, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24, 25, 26, 28, 30, 31, 32, 33, 35, 37, 39, 40, 41, 43, 45, 47, 49, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70

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OFFSET

0,6

COMMENTS

Number of partitions of n into parts 1, 5 and 6. - Hoang Xuan Thanh, Aug 09 2025

LINKS

Table of n, a(n) for n=0..59.

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

FORMULA

a(n) = +a(n-1) +a(n-5) -a(n-7) -a(n-11) +a(n-12). - R. J. Mathar, Aug 21 2014

a(n) = floor((n^2+12*n+72)/60 - (2/5)*[(n mod 5)=4]). - Hoang Xuan Thanh, May 22 2025

MATHEMATICA

CoefficientList[Series[1/((1-x)(1-x^5)(1-x^6)), {x, 0, 60}], x] (* Harvey P. Dale, Mar 06 2011 *)

LinearRecurrence[{1, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 1}, {1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 4, 5}, 70] (* Harvey P. Dale, Feb 09 2015 *)

PROG

(PARI) Vec(1/((1-x)*(1-x^5)*(1-x^6)) + O(x^60)) \\ Hoang Xuan Thanh, Aug 09 2025

(PARI) a(n) = (n^2 + 12*n + 72 - 24*(n%5>3))\60; \\ Hoang Xuan Thanh, Aug 09 2025

CROSSREFS

Sequence in context: A176001 A194272 A285764 * A120505 A029109 A257998

Adjacent sequences: A025773 A025774 A025775 * A025777 A025778 A025779

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved