A363319 -id:A363319 - cp's OEIS frontend

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

Offset: 1

Clark Kimberling, May 24 2023

nonn

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.

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

Cf. A000290, A001844, A123596, A363268, A363269, A363282, A363319.

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}]

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

A363282 Squares (A000290) and centered squares (A001844), in increasing order (i.e., sorted and without duplicates).

Original entry on oeis.org

1, 4, 5, 9, 13, 16, 25, 36, 41, 49, 61, 64, 81, 85, 100, 113, 121, 144, 145, 169, 181, 196, 221, 225, 256, 265, 289, 313, 324, 361, 365, 400, 421, 441, 481, 484, 529, 545, 576, 613, 625, 676, 685, 729, 761, 784, 841, 900, 925, 961, 1013, 1024, 1089, 1105

Offset: 1

Clark Kimberling, May 25 2023

nonn

This sequence consists of the numbers in A363267 arranged in increasing order. Unlike A363267, this is not a linear recurrence sequence; see A363319.

Cf. A000290, A001844, A363267, A363319.

c[1] = 1; c[2] = 1;
c[n_] := If[OddQ[n], c[n - 2] + n, 2 c[n - 1] - n + 1]
u = Table[c[n], {n, 1, 120}]  (* A363267 *)
Union[u] (* A363282 *)

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

cp's OEIS Frontend

A363267 Squares (A000290) alternating with centered squares (A001844).

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