A360417 a(n) = 8*n^2 - 7*n + 2.

2, 3, 20, 53, 102, 167, 248, 345, 458, 587, 732, 893, 1070, 1263, 1472, 1697, 1938, 2195, 2468, 2757, 3062, 3383, 3720, 4073, 4442, 4827, 5228, 5645, 6078, 6527, 6992, 7473, 7970, 8483, 9012, 9557, 10118, 10695, 11288, 11897, 12522, 13163, 13820, 14493, 15182

Offset: 0

Author

James Propp, Feb 06 2023

Keywords

• nonn
• easy

Comments

This is one of the four quadratic sequences that, interleaved, yield A360418.

Links

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

Crossrefs

Cf. A051870, A125201, A360416, A360418.

Programs

Mathematica

Table[8*n^2 - 7*n + 2, {n, 0, 100}]

Formula

From Elmo R. Oliveira, Jan 28 2025: (Start)

G.f.: (17*x^2-3*x+2)/(1-x)^3.

E.g.f.: exp(x)*(2 + x + 8*x^2).

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

a(n) = A360418(4*n-1) for n>=1. (End)

a(n) = A125201(n) + 1, n >= 1. - Omar E. Pol, Jan 28 2025

Extensions

a(0)=2 prepended and more terms from Alois P. Heinz, Jan 28 2025