A363268 Squares (A000290) alternating with 1+squares (A002522).

1, 1, 4, 2, 9, 5, 16, 10, 25, 17, 36, 26, 49, 37, 64, 50, 81, 65, 100, 82, 121, 101, 144, 122, 169, 145, 196, 170, 225, 197, 256, 226, 289, 257, 324, 290, 361, 325, 400, 362, 441, 401, 484, 442, 529, 485, 576, 530, 625, 577, 676, 626, 729, 677, 784, 730, 841

Offset: 1

Author

Clark Kimberling, May 24 2023

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A000290, A002522, A123596, A363267, A363269, A363283.

Programs

Mathematica

c[1] = 1; c[2] = 1;
c[n_] := If[OddQ[n], c[n - 2] + n, c[n - 1] - n + 2]
Table[c[n], {n, 1, 120}]

Formula

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

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