A025782 Expansion of 1/((1-x)*(1-x^6)*(1-x^7)).

1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 4, 5, 6, 6, 6, 6, 7, 8, 9, 10, 10, 10, 11, 12, 13, 14, 15, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 29, 30, 31, 32, 33, 34, 36, 38, 39, 40, 41, 42, 44, 46, 48, 49, 50, 51, 53, 55, 57, 59, 60, 61, 63, 65, 67, 69, 71

Offset

0,7

Comments

Number of partitions of n into parts 1, 6, and 7. - Joerg Arndt, Oct 12 2014

Links

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

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

Formula

a(n) = (n^2 + 14*n + 7*(2+(n mod 6))*(6-(n mod 6)) -6*(n mod 7)*(7-(n mod 7)))/84. - Hoang Xuan Thanh, Aug 19 2025

Mathematica

CoefficientList[Series[1/((1-x)(1-x^6)(1-x^7)), {x, 0, 60}], x] (* Harvey P. Dale, Dec 30 2021 *)
(* Alternative: *)
LinearRecurrence[{1, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, -1, 1}, {1, 1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3, 4, 5}, 70] (* Harvey P. Dale, Dec 30 2021 *)

Prog

(PARI) a(n)=round((n^2+14*n+18)/84+369830\7^(n%7)%7/7) \\ Tani Akinari, Oct 13 2014
(PARI) a(n) = (n^2 + 14*n + 7*(2+n%6)*(6-n%6))\84 \\ Hoang Xuan Thanh, Aug 19 2025

Crossrefs

Sequence in context: A104406 A080344 A194225 * A120506 A327041 A277267

Adjacent sequences: A025779 A025780 A025781 * A025783 A025784 A025785

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved