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

Author

Omar E. Pol, Feb 12 2015

Keywords

• nonn
• easy
• mult

Comments

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

a(n) are the Engel expansion of A070910. - Benedict W. J. Irwin, Dec 15 2016

Links

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

Crossrefs

Cf. A028310, A070910, A246595. Essentially the same as A000290 and A174902.

Programs

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 *)

PARI

a(n)=max(n,1)^2 \\ Charles R Greathouse IV, Dec 16 2016

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

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

Extensions

Keyword:mult added by Andrew Howroyd, Aug 06 2018