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.
%I A175109 #15 Sep 08 2022 08:45:51
%S A175109 1,13,63,171,365,665,1099,1687,2457,3429,4631,6083,7813,9841,12195,
%T A175109 14895,17969,21437,25327,29659,34461,39753,45563,51911,58825,66325,
%U A175109 74439,83187,92597,102689,113491,125023,137313,150381,164255,178955
%N A175109 a(n) = ((2*n+1)^3+(-1)^n)/2.
%C A175109 Partial sums of A110907. Convolution of the finite sequence (1,10,26,10,1) with A002623.
%H A175109 Vincenzo Librandi, <a href="/A175109/b175109.txt">Table of n, a(n) for n = 0..1000</a>
%H A175109 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2,-2,3,-1).
%F A175109 a(n) = 3*a(n-1) -2*a(n-2) -2*a(n-3) +3*a(n-4) -a(n-5).
%F A175109 G.f.: (x^2+4*x+1)*(x^2+6*x+1)/((1+x)*(x-1)^4).
%p A175109 A175109:=n->((2*n+1)^3+(-1)^n)/2: seq(A175109(n), n=0..50); # _Wesley Ivan Hurt_, Apr 18 2017
%t A175109 CoefficientList[Series[(x^2 + 4*x + 1)*(x^2 + 6*x + 1)/((1 + x)*(x - 1)^4), {x, 0, 40}], x] (* _Vincenzo Librandi_, Dec 19 2012 *)
%o A175109 (Magma) I:=[1, 13, 63, 171, 365]; [n le 5 select I[n] else 3*Self(n-1) - 2*Self(n-2) - 2*Self(n-3) + 3*Self(n-4) - Self(n-5): n in [1..40]]; // _Vincenzo Librandi_, Dec 19 2012
%Y A175109 Cf. A002623, A110907.
%K A175109 easy,nonn
%O A175109 0,2
%A A175109 _R. J. Mathar_, Feb 13 2010