cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A011850 a(n) = floor(binomial(n,4)/4).

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%I A011850 #20 Aug 07 2017 23:46:38
%S A011850 0,0,0,0,0,1,3,8,17,31,52,82,123,178,250,341,455,595,765,969,1211,
%T A011850 1496,1828,2213,2656,3162,3737,4387,5118,5937,6851,7866,8990,10230,
%U A011850 11594,13090,14726,16511,18453,20562
%N A011850 a(n) = floor(binomial(n,4)/4).
%H A011850 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-6,6,-10,10,-6,6,-10,10,-6,6,-10,10,-5,1).
%F A011850 a(n) = +5*a(n-1) -10*a(n-2) +10*a(n-3) -6*a(n-4) +6*a(n-5) -10*a(n-6) +10*a(n-7) -6*a(n-8) +6*a(n-9) -10*a(n-10) +10*a(n-11) -6*a(n-12) +6*a(n-13) -10*a(n-14) +10*a(n-15) -5*a(n-16) +a(n-17). [_R. J. Mathar_, Apr 15 2010]
%F A011850 G.f.: x^5*(-3*x^7-3*x^3+3*x^8-2*x^9+x^10-x^5+2*x^6-2*x+3*x^2+2*x^4+1) / ( (1-x)^5*(x^4+1)*(x^8+1) ). [_R. J. Mathar_, Apr 15 2010]
%p A011850 seq(floor(binomial(n,4)/4), n=0.. 39); # _Zerinvary Lajos_, Jan 12 2009
%t A011850 Floor[Binomial[Range[0,50],4]/4] (* or *) LinearRecurrence[ {5,-10,10,-6,6,-10,10,-6,6,-10,10,-6,6,-10,10,-5,1},{0,0,0,0,0,1,3,8,17,31,52,82,123,178,250,341,455},50] (* _Harvey P. Dale_, Mar 25 2013 *)
%Y A011850 A column of triangle A011857.
%K A011850 nonn,easy
%O A011850 0,7
%A A011850 _N. J. A. Sloane_