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A363283 Squares (A000290) and (1+squares) (A002522), in increasing order.

%I A363283 #21 Aug 28 2024 09:37:41
%S A363283 1,2,4,5,9,10,16,17,25,26,36,37,49,50,64,65,81,82,100,101,121,122,144,
%T A363283 145,169,170,196,197,225,226,256,257,289,290,324,325,361,362,400,401,
%U A363283 441,442,484,485,529,530,576,577,625,626,676,677,729,730,784,785
%N A363283 Squares (A000290) and (1+squares) (A002522), in increasing order.
%C A363283 This sequence consists of the numbers in A363268 arranged in increasing order. This sequence and A363268 have the same linear recurrence (in contrast to these pairs: A363267 and A363282; and A363269 and A363283).
%H A363283 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A363283 a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).
%F A363283 G.f.: x*(-1 - x + x^3 - x^4)/((-1 + x)^3 (1 + x)^2).
%F A363283 a(n) = ((2n^2 + 2n + 5) - (2n - 3)*(-1)^n)/8. - _Aaron J Grech_, Aug 26 2024
%F A363283 E.g.f.: ((4 + 3*x + x^2)*cosh(x) + (1 + x + x^2)*sinh(x) - 4)/4. - _Stefano Spezia_, Aug 27 2024
%t A363283 c[1] = 1; c[2] = 1;
%t A363283 c[n_] := If[OddQ[n], c[n - 2] + n, c[n - 1] - n + 2]
%t A363283 u = Table[c[n], {n, 1, 120}] (* A363268 *)
%t A363283 Union[u]   (* this sequence *)
%Y A363283 Cf. A000290, A002522, A363267, A363282, A363268.
%K A363283 nonn,easy
%O A363283 1,2
%A A363283 _Clark Kimberling_, May 25 2023
%E A363283 Definition corrected by _N. J. A. Sloane_, Jun 12 2023