A011942 a(n) = floor( n*(n-1)*(n-2)*(n-3)/32 ).

0, 0, 0, 0, 0, 3, 11, 26, 52, 94, 157, 247, 371, 536, 750, 1023, 1365, 1785, 2295, 2907, 3633, 4488, 5486, 6641, 7969, 9487, 11212, 13162, 15356, 17813, 20553, 23598, 26970, 30690, 34782, 39270, 44178, 49533, 55361, 61688, 68542, 75952, 83947, 92557, 101813, 111746, 122388, 133773, 145935, 158907, 172725

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 (5,-10,10,-6,6,-10,10,-6,6,-10,10,-6,6,-10,10,-5,1).

Crossrefs

Cf. A011915.

Programs

Magma

[Floor(3*Binomial(n,4)/4): n in [0..60]]; // G. C. Greubel, Oct 26 2024

Mathematica

Floor[3*Binomial[Range[0,60], 4]/4] (* G. C. Greubel, Oct 26 2024 *)

SageMath

[3*binomial(n,4)//4 for n in range(61)] # G. C. Greubel, Oct 26 2024

Formula

From R. J. Mathar, Apr 15 2010: (Start)

a(n) = +5*a(n-1) -10*a(n-2) +10*a(n-3) -6*a(n-4) +6*a(n-5) -10*a(n-6) +10*a(n-7) -6*a(n-8) +6*a(n-9) -10*a(n-10) +10*a(n-11) -6*a(n-12) +6*a(n-13) -10*a(n-14) +10*a(n-15) -5*a(n-16) +a(n-17).

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

Extensions

More terms added by G. C. Greubel, Oct 26 2024