A011936 a(n) = floor( n*(n-1)*(n-2)*(n-3)/26 ).

0, 0, 0, 0, 0, 4, 13, 32, 64, 116, 193, 304, 456, 660, 924, 1260, 1680, 2196, 2824, 3577, 4472, 5524, 6752, 8173, 9808, 11676, 13800, 16200, 18900, 21924, 25296, 29044, 33193, 37772, 42808, 48332, 54373, 60964, 68136, 75924, 84360, 93480, 103320, 113916, 125308, 137533, 150632, 164644, 179612, 195577

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..2500
• Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1,0,0,0,0,0,0,0,0,1,-4,6,-4,1).

Crossrefs

Cf. A011915.

Programs

Magma

[Floor(12*Binomial(n,4)/13): n in [0..80]]; // G. C. Greubel, Oct 29 2024

Maple

A011936:=n->floor(n*(n-1)*(n-2)*(n-3)/26): seq(A011936(n), n=0..100); # Wesley Ivan Hurt, Feb 03 2017

Mathematica

Floor[12*Binomial[Range[0,80], 4]/13] (* G. C. Greubel, Oct 29 2024 *)

SageMath

[12*binomial(n,4)//13 for n in range(81)] # G. C. Greubel, Oct 29 2024

Formula

From Chai Wah Wu, Aug 02 2020: (Start)

a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + a(n-13) - 4*a(n-14) + 6*a(n-15) - 4*a(n-16) + a(n-17) for n > 16.

G.f.: x^5*(4 -3*x +4*x^2 -2*x^3 +4*x^4 -2*x^5 +4*x^6 -2*x^7 +4*x^8 -3*x^9 +4*x^10)/((1-x)^4*(1-x^13)). (End)

Extensions

More terms added by G. C. Greubel, Oct 29 2024