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.

A140147 a(1)=1, a(n)=a(n-1)+n^1 if n odd, a(n)=a(n-1)+ n^5 if n is even.

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%I A140147 #10 Jan 02 2024 09:01:13
%S A140147 1,33,36,1060,1065,8841,8848,41616,41625,141625,141636,390468,390481,
%T A140147 928305,928320,1976896,1976913,3866481,3866500,7066500,7066521,
%U A140147 12220153,12220176,20182800,20182825,32064201,32064228,49274596,49274625
%N A140147 a(1)=1, a(n)=a(n-1)+n^1 if n odd, a(n)=a(n-1)+ n^5 if n is even.
%H A140147 Harvey P. Dale, <a href="/A140147/b140147.txt">Table of n, a(n) for n = 1..1000</a>
%F A140147 G.f.: -x*(1+32*x-3*x^2+832*x^3+2*x^4+2112*x^5+2*x^6+832*x^7-3*x^8+32*x^9+x^10)/ ((1+x)^6*(x-1)^7). [From _R. J. Mathar_, Feb 22 2009]
%t A140147 a = {}; r = 1; s = 5; Do[k = 0; Do[k = k + (Sin[Pi m/2]^2) m^r + (Cos[Pi m/2]^2) m^s, {m, 1, n}]; AppendTo[a, k], {n, 1, 100}]; a (*Artur Jasinski*)
%t A140147 nxt[{n_,a_}]:=If[OddQ[n+1],{n+1,a+n+1},{n+1,a+(n+1)^5}]; Transpose[ NestList[ nxt,{1,1},30]][[2]] (* _Harvey P. Dale_, Jun 27 2012 *)
%Y A140147 Cf. A000027, A000217, A000330, A000537, A000538, A000539, A136047, A140113.
%K A140147 nonn
%O A140147 1,2
%A A140147 _Artur Jasinski_, May 12 2008