A083232 a(n) = (3*7^n+(-1)^n)/4.

1, 5, 37, 257, 1801, 12605, 88237, 617657, 4323601, 30265205, 211856437, 1482995057, 10380965401, 72666757805, 508667304637, 3560671132457, 24924697927201, 174472885490405, 1221310198432837, 8549171389029857

Offset: 0

Author

Paul Barry, Apr 23 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A053524 (without leading zero).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (6,7).

Crossrefs

Cf. A083233.

Programs

Magma

[(3*7^n+(-1)^n)/4: n in [0..25]]; // Vincenzo Librandi, Jun 29 2011

PARI

Vec((1-x)/((1-7*x)*(1+x)) + O(x^40)) \\ Andrew Howroyd, Feb 16 2018

Formula

a(n) = (3*7^n+(-1)^n)/4.

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

E.g.f.: (3*exp(7*x)+exp(-x))/4