A011937 a(n) = floor( n*(n-1)*(n-2)*(n-3)/27 ).

0, 0, 0, 0, 0, 4, 13, 31, 62, 112, 186, 293, 440, 635, 889, 1213, 1617, 2115, 2720, 3445, 4306, 5320, 6502, 7871, 9445, 11244, 13288, 15600, 18200, 21112, 24360, 27968, 31964, 36373, 41223, 46542, 52360, 58706, 65613, 73112, 81235, 90017, 99493, 109697, 120667, 132440, 145053, 158546, 172960, 188334

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,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-4,6,-4,1).

Crossrefs

Cf. A011915.

Programs

Magma

[Floor(8*Binomial(n,4)/9): n in [0..80]]; // G. C. Greubel, Oct 29 2024

Mathematica

Table[Floor[n (n-1)(n-2)(n-3)/27], {n, 0, 60}] (* Wesley Ivan Hurt, Jan 02 2024 *)

PARI

a(n)=n*(n-1)*(n-2)*(n-3)\27 \\ Charles R Greathouse IV, Oct 18 2022

SageMath

[8*binomial(n,4)//9 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-27) - 4*a(n-28) + 6*a(n-29) - 4*a(n-30) + a(n-31) for n > 30.

G.f.: x^5*(4 -3*x +3*x^2 +2*x^4 -x^5 +4*x^6 -2*x^7 +x^8 +3*x^9 -x^11 +4*x^12 -x^13 +3*x^15 +x^16 -2*x^17 +4*x^18 -x^19 +2*x^20 +3*x^22 -3*x^23 +4*x^24)/((1-x)^5*(1 +x +x^2)*(1 +x^3 +x^6)*(1 +x^9 +x^18)). (End)

Extensions

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