A234277 a(n) = binomial(floor(n/2),4) + (ceiling(n/2)-3)*binomial(floor(n/2),3).

0, 0, 0, 0, 0, 0, 0, 1, 5, 9, 25, 35, 75, 95, 175, 210, 350, 406, 630, 714, 1050, 1170, 1650, 1815, 2475, 2695, 3575, 3861, 5005, 5369, 6825, 7280, 9100, 9660, 11900, 12580, 15300, 16116, 19380, 20349, 24225, 25365, 29925, 31255, 36575, 38115, 44275, 46046, 53130, 55154, 63250, 65550, 74750, 77350, 87750, 90675

Offset: 0

Author

N. J. A. Sloane, Dec 27 2013

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Dhruv Mubayi, Counting substructures II: Hypergraphs, Combinatorica 33 (2013), no. 5, 591--612. MR3132928.
• Index entries for linear recurrences with constant coefficients, signature (1,4,-4,-6,6,4,-4,-1,1).

Crossrefs

Cf. A000292, A002418.

Programs

Mathematica

CoefficientList[Series[-x^7 (4 x + 1)/((x - 1)^5 (x + 1)^4), {x, 0, 40}], x] (* Vincenzo Librandi Feb 01 2014 *)
LinearRecurrence[{1,4,-4,-6,6,4,-4,-1,1},{0,0,0,0,0,0,0,1,5},60] (* Harvey P. Dale, Jun 27 2020 *)

PARI

Vec(-x^7*(4*x+1)/((x-1)^5*(x+1)^4) + O(x^100)) \\ Colin Barker, Jan 02 2014

Formula

G.f.: -x^7*(4*x+1) / ((x-1)^5*(x+1)^4). - Colin Barker, Jan 02 2014

a(n) = (2*n - 1 + (-1)^n)*(2*n - 5 + (-1)^n)*(2*n - 9 + (-1)^n)*(10*n - 57 - 3*(-1)^n)/6144. - Luce ETIENNE, Nov 18 2017