A011937 - OEIS

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

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OFFSET

0,6

LINKS

Table of n, a(n) for n=0..36.

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).

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

MATHEMATICA

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

PROG

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

CROSSREFS

Sequence in context: A097120 A098536 A216563 * A307304 A097122 A116411

Adjacent sequences: A011934 A011935 A011936 * A011938 A011939 A011940

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved