A025807 Expansion of 1/((1-x^2)*(1-x^5)*(1-x^7)).

1, 0, 1, 0, 1, 1, 1, 2, 1, 2, 2, 2, 3, 2, 4, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 13, 13, 14, 14, 15, 16, 16, 18, 17, 19, 19, 20, 21, 21, 23, 23, 24, 25, 25, 27, 27, 29, 29, 30, 31, 32, 33, 34, 35

Offset

0,8

Comments

Number of partitions of n into parts 2, 5, and 7. - Hoang Xuan Thanh, Aug 26 2025

Links

Table of n, a(n) for n=0..63.

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

Formula

a(n) = floor((n^2 +14*n +123 +17*(-1)^n +28*[(n mod 5) in {2,4}] -56*[(n mod 5)=3])/140). - Hoang Xuan Thanh, Aug 26 2025

Mathematica

CoefficientList[Series[1/((1-x^2)(1-x^5)(1-x^7)), {x, 0, 70}], x] (* Harvey P. Dale, Sep 05 2017 *)
(* Alternative: *)
LinearRecurrence[{0, 1, 0, 0, 1, 0, 0, 0, -1, 0, 0, -1, 0, 1}, {1, 0, 1, 0, 1, 1, 1, 2, 1, 2, 2, 2, 3, 2}, 70] (* Harvey P. Dale, Sep 05 2017 *)

Prog

(PARI) a(n) = (n^2 + 14*n + 84 -35*(n%2) +28*[2, 2, 3, 0, 3][n%5+1])\140 \\ Hoang Xuan Thanh, Aug 26 2025

Crossrefs

Sequence in context: A029232 A221531 A282970 * A120254 A263020 A068796

Adjacent sequences: A025804 A025805 A025806 * A025808 A025809 A025810

Keyword

nonn,easy,changed

Author

N. J. A. Sloane

Status

approved