A011933 a(n) = floor( n*(n-1)*(n-2)*(n-3)/23 ).

0, 0, 0, 0, 1, 5, 15, 36, 73, 131, 219, 344, 516, 746, 1044, 1424, 1899, 2483, 3193, 4044, 5055, 6245, 7633, 9240, 11088, 13200, 15600, 18313, 21365, 24783, 28596, 32833, 37523, 42699, 48392, 54636, 61466, 68916, 77024, 85827, 95363, 105673, 116796, 128775, 141653, 155473, 170280, 186120, 203040, 221088

Offset: 0

Author

N. J. A. Sloane

Keywords

• easy
• nonn

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

Crossrefs

Cf. A000332, A011915, A052762.

Programs

Magma

[Floor(24*Binomial(n,4)/23): n in [0..80]]; // G. C. Greubel, Nov 03 2024

Mathematica

Table[Floor[(n(n-1)(n-2)(n-3))/23],{n,0,60}] (* Harvey P. Dale, Jun 22 2011 *)

PARI

a(n) = n*(n-1)*(n-2)*(n-3)\23; \\ Michel Marcus, Jun 14 2017

SageMath

[24*binomial(n,4)//23 for n in range(81)] # G. C. Greubel, Nov 03 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-23) - 4*a(n-24) + 6*a(n-25) - 4*a(n-26) + a(n-27) for n > 26.

G.f.: x^4*(1+x^2)*(1 + x + x^3 - x^5 + 4*x^6 - x^7 - x^8 + 2*x^9 + 2*x^11 - x^12 - x^13 + 4*x^14 - x^15 + x^17 + x^19 + x^20)/((1-x)^4*(1-x^23)). (End)

Extensions

More terms added by G. C. Greubel, Nov 03 2024