A360416 a(n) = 8*n^2 - 9*n + 3.

3, 2, 17, 48, 95, 158, 237, 332, 443, 570, 713, 872, 1047, 1238, 1445, 1668, 1907, 2162, 2433, 2720, 3023, 3342, 3677, 4028, 4395, 4778, 5177, 5592, 6023, 6470, 6933, 7412, 7907, 8418, 8945, 9488, 10047, 10622, 11213, 11820, 12443, 13082, 13737, 14408, 15095

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. A360417, A360418.

Programs

Mathematica

Table[8*n^2 - 9*n + 3, {n, 0, 100}]

Formula

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

G.f.: (3 - 7*x + 20*x^2)/(1 - x)^3.

E.g.f.: (3 - x + 8*x^2)*exp(x).

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

a(n) = A360418(4*n-2) for n >= 1. (End)

Extensions

a(0)=3 prepended and more terms from Elmo R. Oliveira, Jan 28 2025