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a(n) = floor(binomial(n,5)/6).
1

%I #18 Jun 13 2023 09:24:08

%S 0,0,0,0,0,0,1,3,9,21,42,77,132,214,333,500,728,1031,1428,1938,2584,

%T 3391,4389,5608,7084,8855,10963,13455,16380,19792,23751,28318,33562,

%U 39556,46376,54105,62832,72649,83657

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

%H <a href="/index/Rec#order_59">Index entries for linear recurrences with constant coefficients</a>, 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).

%F 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]

%F a(n) = floor(binomial(n+1,6)/(n+1)). [_Gary Detlefs_, Nov 23 2011]

%p seq(floor(binomial(n,5)/6), n=0..38); # _Zerinvary Lajos_, Jan 12 2009

%Y A column of triangle A011847.

%K nonn

%O 0,8

%A _N. J. A. Sloane_