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A363283
Squares (A000290) and (1+squares) (A002522), in increasing order.
2
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
1,2
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).
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
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 *)
CROSSREFS
Sequence in context: A282737 A039891 A280729 * A213011 A175265 A320225
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 25 2023
EXTENSIONS
Definition corrected by N. J. A. Sloane, Jun 12 2023
STATUS
approved

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Last modified September 20 20:29 EDT 2024. Contains 376078 sequences. (Running on oeis4.)