A175111 a(n) = ((2*n+1)^5+(-1)^n)/2.

1, 121, 1563, 8403, 29525, 80525, 185647, 379687, 709929, 1238049, 2042051, 3218171, 4882813, 7174453, 10255575, 14314575, 19567697, 26260937, 34671979, 45112099, 57928101, 73504221, 92264063, 114672503, 141237625, 172512625

Offset

0,2

Comments

Partial sums of A175112.

Convolution of the finite sequence 1,116,967,1672,967,116,1 with A001753.

Links

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

Index entries for linear recurrences with constant coefficients, signature (5,-9,5,5,-9,5,-1).

Formula

a(n) = 5*a(n-1) -9*a(n-2) +5*a(n-3) +5*a(n-4) -9*a(n-5) +5*a(n-6) -a(n-7).

G.f: (1+116*x+967*x^2+1672*x^3+967*x^4+116*x^5+x^6)/((1+x)*(x-1)^6).

Mathematica

CoefficientList[Series[(1 + 116*x + 967*x^2 + 1672*x^3 + 967*x^4 + 116*x^5 + x^6)/((1 + x)*(x - 1)^6), {x, 0, 40}], x] (* Vincenzo Librandi, Dec 19 2012 *)
LinearRecurrence[{5, -9, 5, 5, -9, 5, -1}, {1, 121, 1563, 8403, 29525, 80525, 185647}, 50] (* Harvey P. Dale, May 30 2014 *)

Prog

(Magma) I:=[1, 121, 1563, 8403, 29525, 80525, 185647]; [n le 7 select I[n] else 5*Self(n-1) - 9*Self(n-2) + 5*Self(n-3) + 5*Self(n-4) - 9*Self(n-5) + 5*Self(n-6) - Self(n-7): n in [1..40]]; // Vincenzo Librandi, Dec 19 2012

Crossrefs

Sequence in context: A066444 A206466 A137434 * A115190 A231706 A189652

Adjacent sequences: A175108 A175109 A175110 * A175112 A175113 A175114

Keyword

easy,nonn

Author

R. J. Mathar, Feb 13 2010

Status

approved