|
| |
|
|
A092531
|
|
Expansion of (1+x^10)/((1-x)*(1-x^4)^2*(1-x^8)).
|
|
0
|
|
|
|
1, 1, 1, 1, 3, 3, 3, 3, 7, 7, 8, 8, 14, 14, 16, 16, 25, 25, 29, 29, 41, 41, 47, 47, 63, 63, 72, 72, 92, 92, 104, 104, 129, 129, 145, 145, 175, 175, 195, 195, 231, 231, 256, 256, 298, 298, 328, 328, 377, 377, 413, 413, 469, 469, 511, 511, 575, 575, 624, 624, 696, 696, 752, 752
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,5
|
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (1,1,-1,1,-1,-1,1,1,-1,-1,1,-1,1,1,-1).
|
|
|
FORMULA
|
G.f.: ( 1+x^4+x^8-x^2-x^6 ) / ( (1+x^4) * (1+x^2)^2 * (1+x)^3 * (1-x)^4 ). - R. J. Mathar, Dec 18 2014
a(n) = (2*n^3 + 21*n^2 + 175*n + 441 + 3*(n^2 + 7*n + 29)*(-1)^n + 30*(2*n + 7)*(-1)^((2*n - 1 + (-1)^n)/4) + 30*(-1)^((6*n - 1 + (-1)^n)/4) + 48*((-1)^((2*n - 3 + (-1)^n + 2*(-1)^((2*n - 1 + (-1)^n)/4))/8) - (-1)^((6*n - 5 + 3*(-1)^n + 2*(-1)^((2*n - 1 + (-1)^n)/4))/8)))/768. - Luce ETIENNE, Mar 31 2015
Shorter version of above:
a(n) = (2*n^3 + 21*n^2 + 175*n + 441 + 3*(n^2 + 7*n + 29)*(-1)^n + 30*(2*n + 7)*sign(1-n%4+n%2) + 30*sign(2-(n+1)%4-n%2) + 48*((5*n-n^2)%4)*sign(5-n%8))/768, where sign(x) = x/abs(x), and a%b = a (mod b). - Derek Orr, Apr 05 2015
|
|
|
MATHEMATICA
|
CoefficientList[Series[(1 + x^4 + x^8 - x^2 - x^6) / ((x^4 + 1) (1 + x^2)^2 (1 + x)^3 (x-1)^4), {x, 0, 70}], x] (* Vincenzo Librandi, Apr 05 2015 *)
|
|
|
PROG
|
(PARI) Vec((1+x^10)/((1-x)*(1-x^4)^2*(1-x^8)) + O(x^80)) \\ Michel Marcus, Apr 05 2015
(PARI)
a(n) = (2*n^3 + 21*n^2 + 175*n + 441 + 3*(n^2 + 7*n + 29)*(-1)^n + 30*(2*n + 7)*sign(1-n%4+n%2) + 30*sign(2-(n+1)%4-n%2) + 48*((5*n-n^2)%4)*sign(5-n%8))/768
vector(100, n, a(n-1)) \\ Derek Orr, Apr 05 2015
(Magma) m:=70; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1+x^4+x^8-x^2-x^6)/((1+x^4)*(1+x^2)^2*(1+x)^3*(1-x)^4))); // Bruno Berselli, Apr 07 2015
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
