A175798 Expansion of ( -3+x+4*x^2-3*x^3+3*x^5-x^7-3*x^4+x^6 ) / ( (1+x) *(x^5-x^4-x^3+x^2-1) *(x-1)^2 ).

3, 2, 4, 2, 4, 3, 5, 6, 6, 8, 5, 8, 5, 9, 9, 10, 13, 7, 14, 4, 16, 8, 18, 15, 12, 19, 2, 25, 2, 32, 11, 24, 20, 1, 36, -13, 59, -10, 58, 1, 18, 34, -28, 96, -55, 132, -64, 88, -19, -9, 116

Offset

0,1

Links

Table of n, a(n) for n=0..50.

Index entries for linear recurrences with constant coefficients, signature (1,2,-3,-1,4,-1,-2,1).

Formula

a(n)= +a(n-1) +2*a(n-2) -3*a(n-3) -a(n-4) +4*a(n-5) -a(n-6) -2*a(n-7) +a(n-8).

Mathematica

f[x_] = Expand[(1 - x^2 + x^3 + x^4 - x^5)*(-x^2 + x^3 + x^4 - x^5)];
a = Table[SeriesCoefficient[Series[-1/f[x], {x, 0, 50}], n], {n, 0, 50}]
LinearRecurrence[{1, 2, -3, -1, 4, -1, -2, 1}, {3, 2, 4, 2, 4, 3, 5, 6}, 60] (* Harvey P. Dale, Apr 09 2023 *)

Crossrefs

Sequence in context: A328052 A089214 A057038 * A294111 A349322 A193295

Adjacent sequences: A175795 A175796 A175797 * A175799 A175800 A175801

Keyword

sign,easy

Author

Roger L. Bagula, Dec 04 2010

Status

approved