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URL: https://oeis.org/A363268

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A363268
Squares (A000290) alternating with 1+squares (A002522).
4
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
1,3
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).
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}]
With[{nn=30}, Riffle[Range[nn]^2, Range[0, nn-1]^2+1]] (* or *) LinearRecurrence[{1, 2, -2, -1, 1}, {1, 1, 4, 2, 9}, 70] (* Harvey P. Dale, Mar 04 2026 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 24 2023
STATUS
approved