A029064 Expansion of 1/((1-x)*(1-x^4)*(1-x^5)*(1-x^7)).

1, 1, 1, 1, 2, 3, 3, 4, 5, 6, 7, 8, 10, 11, 13, 15, 17, 19, 21, 24, 27, 30, 33, 36, 40, 44, 48, 52, 57, 62, 67, 72, 78, 84, 90, 97, 104, 111, 118, 126, 135, 143, 152, 161, 171, 181, 191, 202, 213, 225, 237, 249, 262

Offset

0,5

Comments

Number of partitions of n into parts 1, 4, 5 and 7. - Ilya Gutkovskiy, May 17 2017

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = floor((2*n^3+51*n^2+388*n+1680)/1680). - Tani Akinari, May 23 2014

a(-17 - n) = -a(n). - Michael Somos, May 23 2014

Example

G.f. = 1 + x + x^2 + x^3 + 2*x^4 + 3*x^5 + 3*x^6 + 4*x^7 + 5*x^8 + 6*x^9 + ...

Mathematica

a[ n_] := Quotient[ 2 n^3 + 51 n^2 + 388 n, 1680] + 1; (* Michael Somos, May 23 2014 *)
CoefficientList[Series[1/((1 - x)*(1 - x^4)*(1 - x^5)*(1 - x^7)), {x, 0, 50}], x] (* G. C. Greubel, May 17 2017 *)

Prog

(PARI) {a(n) = (2*n^3 + 51*n^2 + 388*n) \ 1680 + 1}; /* Michael Somos, May 23 2014 */
(PARI) x='x+O('x^50); Vec(1/((1 - x)*(1 - x^4)*(1 - x^5)*(1 - x^7))) \\ G. C. Greubel, May 17 2017

Crossrefs

Sequence in context: A017886 A029038 A011877 * A029037 A017875 A039732

Adjacent sequences: A029061 A029062 A029063 * A029065 A029066 A029067

Keyword

nonn

Author

N. J. A. Sloane, Dec 11 1999

Status

approved