A363267 - OEIS

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A363267

Squares (A000290) alternating with centered squares (A001844).

1, 1, 4, 5, 9, 13, 16, 25, 25, 41, 36, 61, 49, 85, 64, 113, 81, 145, 100, 181, 121, 221, 144, 265, 169, 313, 196, 365, 225, 421, 256, 481, 289, 545, 324, 613, 361, 685, 400, 761, 441, 841, 484, 925, 529, 1013, 576, 1105, 625, 1201, 676, 1301, 729, 1405, 784

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OFFSET

1,3

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..55.

Index entries for linear recurrences with constant coefficients, signature (0,3,0,-3,0,1).

FORMULA

a(n) = 3*a(n-2) - 3*a(n-4) + a(n-6).

G.f.: x*(-1 - x - x^2 - 2 x^3 - x^5)/(-1 + x^2)^3.

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

MATHEMATICA

c[1] = 1; c[2] = 1;

c[n_] := If[OddQ[n], c[n - 2] + n, 2 c[n - 1] - n + 1]

Table[c[n], {n, 1, 120}]

CROSSREFS