A273366 a(n) = 10*n^2 + 10*n + 2.

2, 22, 62, 122, 202, 302, 422, 562, 722, 902, 1102, 1322, 1562, 1822, 2102, 2402, 2722, 3062, 3422, 3802, 4202, 4622, 5062, 5522, 6002, 6502, 7022, 7562, 8122, 8702, 9302, 9922, 10562, 11222, 11902, 12602, 13322, 14062, 14822, 15602

Offset: 0

Author

Nathan Fox, Brooke Logan, and N. J. A. Sloane, May 20 2016

Keywords

• nonn
• easy

Comments

These are the numbers k such that 10*k+5 is a perfect square.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A062786, A132356, A273365, A273367, A273368, A350760.

Cf. A033583 (perfect squares ending in 0 in base 10 with final 0 removed).

Programs

Mathematica

LinearRecurrence[{3,-3,1}, {2, 22, 62}, 50] (* G. C. Greubel, May 20 2016 *)
Table[10n^2+10n+2,{n,0,40}] (* Harvey P. Dale, May 21 2024 *)

PARI

a(n)=10*n^2+10*n+2 \\ Charles R Greathouse IV, Jan 31 2017

Formula

G.f.: 2*(x^2+8x+1)/(1-x)^3.

From G. C. Greubel, May 20 2016: (Start)

E.g.f.: 2*(1 + 10*x + 5*x^2)*exp(x).

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)

a(n) = 2*A062786(n+1). - R. J. Mathar, Jun 03 2016

Sum_{n>=0} 1/a(n) = Pi/(2*sqrt(5)) * tan(Pi/(2*sqrt(5))) (A350760). - Amiram Eldar, Jan 20 2022