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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• 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).

Crossrefs

A column of triangle A011847.

Programs

Maple

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

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]