A011843 a(n) = floor(binomial(n,5)/6).

0, 0, 0, 0, 0, 0, 1, 3, 9, 21, 42, 77, 132, 214, 333, 500, 728, 1031, 1428, 1938, 2584, 3391, 4389, 5608, 7084, 8855, 10963, 13455, 16380, 19792, 23751, 28318, 33562, 39556, 46376, 54105, 62832, 72649, 83657, 95959, 109668, 124899, 141778, 160433, 181001, 203626

Offset

0,8

Links

Andrew Howroyd, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -5, 10, -10, 5, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 5, -10, 10, -5, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -5, 10, -10, 5, -1).

Formula

a(n) = +5*a(n-1) -10*a(n-2) +10*a(n-3) -5*a(n-4) +a(n-5) +a(n-18) -5*a(n-19) +10*a(n-20) -10*a(n-21) +5*a(n-22) -a(n-23) -a(n-36) +5*a(n-37) -10*a(n-38) +10*a(n-39) -5*a(n-40) +a(n-41) +a(n-54) -5*a(n-55) +10*a(n-56) -10*a(n-57) +5*a(n-58) -a(n-59). - R. J. Mathar, Apr 15 2010

a(n) = floor(binomial(n+1,6)/(n+1)). - Gary Detlefs, Nov 23 2011

Maple

seq(floor(binomial(n, 5)/6), n=0..38); # Zerinvary Lajos, Jan 12 2009

Mathematica

Quotient[Binomial[Range[0, 50], 5], 6] (* Paolo Xausa, May 29 2026 *)

Prog

(PARI) a(n)=binomial(n, 5)\6 \\ Charles R Greathouse IV, May 28 2026

Crossrefs

A column of triangle A011847.

Sequence in context: A161214 A354961 A213396 * A080549 A175006 A084569

Adjacent sequences: A011840 A011841 A011842 * A011844 A011845 A011846

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from Andrew Howroyd, Oct 22 2025

Status

approved