A253909 1 together with the positive squares.

1, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, 484, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1024, 1089, 1156, 1225, 1296, 1369, 1444, 1521, 1600, 1681, 1764, 1849, 1936, 2025, 2116, 2209, 2304, 2401, 2500

Offset

0,3

Comments

Also, right border of A246595 arranged as an irregular triangle.

Engel expansion of A070910. - Benedict W. J. Irwin, Dec 15 2016

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

Formula

a(n) = A028310(n)^2.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>=4. - David Neil McGrath, May 23 2015

G.f.: (1 - 2*x + 4*x^2 - x^3)/(1-x)^3. - David Neil McGrath, May 25 2015

E.g.f.: 1 + exp(x)*x*(1 + x). - Stefano Spezia, Jan 30 2023

Mathematica

Join[{1}, Range[50]^2] (* Alonso del Arte, Feb 23 2015 *)
Range[0, 50]^2 /. 0 -> 1 (* Robert G. Wilson v, Dec 15 2016 *)

Prog

(PARI) a(n)=max(n, 1)^2 \\ Charles R Greathouse IV, Dec 16 2016
(Magma)
A253909:= func< n | n^2 +0^n >; // G. C. Greubel, Jan 22 2026
(Python)
def A253909(n): return n**2 +int(n==0) # G. C. Greubel, Jan 22 2026

Crossrefs

Essentially the same as A000290 and A174902.

Cf. A028310, A070910, A246595.

Sequence in context: A174902 A000290 A162395 * A305559 A221222 A144913

Adjacent sequences: A253906 A253907 A253908 * A253910 A253911 A253912

Keyword

nonn,easy,mult

Author

Omar E. Pol, Feb 12 2015

Extensions

Keyword:mult added by Andrew Howroyd, Aug 06 2018

Status

approved