A339048 a(n) = 2*n^2 + 9.

9, 11, 17, 27, 41, 59, 81, 107, 137, 171, 209, 251, 297, 347, 401, 459, 521, 587, 657, 731, 809, 891, 977, 1067, 1161, 1259, 1361, 1467, 1577, 1691, 1809, 1931, 2057, 2187, 2321, 2459, 2601, 2747, 2897, 3051, 3209, 3371, 3537, 3707, 3881

Offset: 0

Author

Wolfdieter Lang, Dec 09 2020

Keywords

• nonn
• easy

Comments

Third diagonal sequence of triangle A338432, for n >= 1.

Links

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

Crossrefs

Cf. A058331, A255843, A255847, A338432.

Programs

Magma

[2*n^2 + 9 : n in [0..50]]; // Wesley Ivan Hurt, May 04 2021

Formula

a(n) = 2*n^2 + 9, n >= 0.

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

a(n) = A338432(n + 2, n), for n >= 1 and a(0) = 9.

G.f.: (9 - 16*x + 11*x^2)/(1 - x)^3.

E.g.f.: exp(x)*(9 + 2*x + 2*x^2). - Stefano Spezia, Aug 07 2024