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.

A302560 Partial sums of icosahedral numbers (A006564).

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%I A302560 #19 Aug 19 2018 09:30:43
%S A302560 1,13,61,185,440,896,1638,2766,4395,6655,9691,13663,18746,25130,33020,
%T A302560 42636,54213,68001,84265,103285,125356,150788,179906,213050,250575,
%U A302560 292851,340263,393211,452110,517390,589496,668888,756041,851445,955605,1069041,1192288,1325896
%N A302560 Partial sums of icosahedral numbers (A006564).
%C A302560 Geometrically, the partial sums of A006564 may be interpreted as 4-dimensional icosahedral hyperpyramidal numbers.
%H A302560 Colin Barker, <a href="/A302560/b302560.txt">Table of n, a(n) for n = 1..1000</a>
%H A302560 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A302560 a(n) = Sum_{k=1..n} A006564(k).
%F A302560 From _Colin Barker_, Aug 15 2018: (Start)
%F A302560 G.f.: x*(1 + 8*x + 6*x^2) / (1 - x)^5.
%F A302560 a(n) = n*(2 - 3*n + 10*n^2 + 15*n^3)/24.
%F A302560 a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.
%F A302560 (End)
%o A302560 (PARI) Vec(x*(1 + 8*x + 6*x^2) / (1 - x)^5 + O(x^40)) \\ _Colin Barker_, Aug 15 2018
%o A302560 (PARI) a(n) = (n*(2 - 3*n + 10*n^2 + 15*n^3)) / 24 \\ _Colin Barker_, Aug 15 2018
%Y A302560 Cf. A006564.
%K A302560 nonn,easy
%O A302560 1,2
%A A302560 _Alejandro J. Becerra Jr._, Aug 15 2018