A102303 a(n) = (1/6) * (7^(n+1) - 3*(-1)^n + 2).

1, 9, 57, 401, 2801, 19609, 137257, 960801, 6725601, 47079209, 329554457, 2306881201, 16148168401, 113037178809, 791260251657, 5538821761601, 38771752331201, 271402266318409, 1899815864228857, 13298711049602001, 93090977347214001, 651636841430498009

Offset: 0

Author

Roger L. Bagula, Mar 15 2005

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (7,1,-7).

Crossrefs

Cf. A000035, A023000.

Programs

Magma

[(7^(n+1)-3*(-1)^n+2)/6: n in [0..50]]; // G. C. Greubel, Feb 03 2024

Mathematica

Table[(7^(n+1) -3*(-1)^n +2)/6, {n, 0, 50}]

SageMath

[(7^(n+1)-3*(-1)^n+2)/6 for n in range(51)] # G. C. Greubel, Feb 03 2024

Formula

From Chai Wah Wu, Mar 11 2021: (Start)

a(n) = 7*a(n-1) + a(n-2) - 7*a(n-3) for n > 2.

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

From G. C. Greubel, Feb 03 2024: (Start)

a(n) = A023000(n+1) + A000035(n).

E.g.f.: (1/6)*(-3*exp(-x) + 2*exp(x) + 7*exp(7*x)). (End)

Extensions

Edited by N. J. A. Sloane, May 29 2007