A029278 Expansion of 1/((1-x^3)(1-x^5)(1-x^7)(1-x^8)).

1, 0, 0, 1, 0, 1, 1, 1, 2, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 7, 7, 8, 9, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, 21, 22, 24, 25, 27, 28, 30, 32, 33, 36, 37, 39, 42, 43, 46, 48, 50, 53, 55, 58, 61, 63, 66, 69, 72, 75, 78, 82, 85, 88, 92, 95, 99, 103, 107

Offset

0,9

Comments

Number of partitions of n into parts 3, 5, 7, and 8. - Vincenzo Librandi, Jun 03 2014

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

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

Formula

Euler transform of length 8 sequence [ 0, 0, 1, 0, 1, 0, 1, 1]. - Michael Somos, Jun 03 2014

G.f.: 1/((1-x^3)*(1-x^5)*(1-x^7)*(1-x^8)). - Michael Somos, Jun 03 2014

a(-23 - n) = - a(n) for all n in Z. - Michael Somos, Jun 03 2014

a(n) = a(n-3) + a(n-5) + a(n-7) - a(n-10) - a(n-11) - a(n-12) - a(n-13) + a(n-16) + a(n-18) + a(n-20) - a(n-23). - Wesley Ivan Hurt, Apr 16 2023

Example

G.f. = 1 + x^3 + x^5 + x^6 + x^7 + 2*x^8 + x^9 + 2*x^10 + 2*x^11 + 2*x^12 + ...

Mathematica

CoefficientList[Series[1/((1 - x^3) (1 - x^5) (1 - x^7) (1 - x^8)), {x, 0, 100}], x] (* Vincenzo Librandi, Jun 03 2014 *)

Prog

(PARI) {a(n) = my(s = n<0); if( s, n = -23 - n); (-1)^s * polcoeff( 1 / ((1 - x^3) * (1 - x^5) * (1 - x^7) * (1 - x^8)) + x * O(x^n), n)}; /* Michael Somos, Jun 03 2014 */

Crossrefs

Sequence in context: A024154 A117875 A084840 * A125950 A323088 A052954

Adjacent sequences: A029275 A029276 A029277 * A029279 A029280 A029281

Keyword

nonn,easy

Author

N. J. A. Sloane.

Status

approved