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 A363267 #16 Jun 15 2023 06:54:19
%S A363267 1,1,4,5,9,13,16,25,25,41,36,61,49,85,64,113,81,145,100,181,121,221,
%T A363267 144,265,169,313,196,365,225,421,256,481,289,545,324,613,361,685,400,
%U A363267 761,441,841,484,925,529,1013,576,1105,625,1201,676,1301,729,1405,784
%N A363267 Squares (A000290) alternating with centered squares (A001844).
%C A363267 This is a linear recurrence sequence. If the terms are arranged in nondecreasing order, the result, A363319, is linearly recurrent. If the terms are arranged in increasing order, so that there are no duplicates, the result, A363282, is not linearly recurrent.
%H A363267 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,3,0,-3,0,1).
%F A363267 a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6).
%F A363267 G.f.: x*(-1 - x - x^2 - 2 x^3 - x^5)/(-1 + x^2)^3.
%F A363267 a(n+1) = n/2+3*n^2/8+3/4+(-1)^n*(1/4+n/2-n^2/8). - _R. J. Mathar_, Jun 15 2023
%t A363267 c[1] = 1; c[2] = 1;
%t A363267 c[n_] := If[OddQ[n], c[n - 2] + n, 2 c[n - 1] - n + 1]
%t A363267 Table[c[n], {n, 1, 120}]
%Y A363267 Cf. A000290, A001844, A123596, A363268, A363269, A363282, A363319.
%K A363267 nonn
%O A363267 1,3
%A A363267 _Clark Kimberling_, May 24 2023