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

1, 2, 4, 5, 9, 10, 16, 17, 25, 26, 36, 37, 49, 50, 64, 65, 81, 82, 100, 101, 121, 122, 144, 145, 169, 170, 196, 197, 225, 226, 256, 257, 289, 290, 324, 325, 361, 362, 400, 401, 441, 442, 484, 485, 529, 530, 576, 577, 625, 626, 676, 677, 729, 730, 784, 785

Offset: 1

Author

Clark Kimberling, May 25 2023

Keywords

• nonn
• easy

Comments

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).

Links

• Index entries for linear recurrences with constant coefficients, signature (1,2,-2,-1,1).

Crossrefs

Cf. A000290, A002522, A363267, A363282, A363268.

Programs

Mathematica

c[1] = 1; c[2] = 1;
c[n_] := If[OddQ[n], c[n - 2] + n, c[n - 1] - n + 2]
u = Table[c[n], {n, 1, 120}] (* A363268 *)
Union[u]   (* this sequence *)

Formula

a(n) = a(n-1) + 2*a(n-2) - 2*a(n-3) - a(n-4) + a(n-5).

G.f.: x*(-1 - x + x^3 - x^4)/((-1 + x)^3 (1 + x)^2).

a(n) = ((2n^2 + 2n + 5) - (2n - 3)*(-1)^n)/8. - Aaron J Grech, Aug 26 2024

E.g.f.: ((4 + 3*x + x^2)*cosh(x) + (1 + x + x^2)*sinh(x) - 4)/4. - Stefano Spezia, Aug 27 2024

Extensions

Definition corrected by N. J. A. Sloane, Jun 12 2023