A111385 a(n) = binomial(n,4) - binomial(floor(n/2),4) - binomial(ceiling(n/2),4).

0, 0, 0, 0, 1, 5, 15, 34, 68, 120, 200, 310, 465, 665, 931, 1260, 1680, 2184, 2808, 3540, 4425, 5445, 6655, 8030, 9636, 11440, 13520, 15834, 18473, 21385, 24675, 28280, 32320, 36720, 41616, 46920, 52785, 59109, 66063, 73530, 81700, 90440, 99960, 110110, 121121

Offset

0,6

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,2,-6,0,6,-2,-2,1).

Formula

a(n) = +2 a(n-1) +2 a(n-2) -6 a(n-3) +6 a(n-5) -2 a(n-6) -2 a(n-7) +a(n-8). - R. J. Mathar, Mar 11 2012

G.f.: x^4*(1 + 3*x + 3*x^2) / ((1 - x)^5*(1 + x)^3). - Colin Barker, Jul 28 2013

From Colin Barker, May 04 2017: (Start)

a(n) = n^2 * (7*n^2 - 36*n + 44) / 192 for n even.

a(n) = (7*n^4 - 36*n^3 + 38*n^2 + 36*n - 45) / 192 for n odd.

(End)

Prog

(PARI) concat(vector(4), Vec(x^4*(1 + 3*x + 3*x^2) / ((1 - x)^5*(1 + x)^3) + O(x^60))) \\ Colin Barker, May 04 2017

Crossrefs

Sequence in context: A162513 A006003 A026101 * A084288 A083049 A015627

Adjacent sequences: A111382 A111383 A111384 * A111386 A111387 A111388

Keyword

nonn,easy

Author

N. J. A. Sloane, Nov 10 2005

Status

approved