A083231 a(n) = (3*5^n + (-3)^n)/4.

1, 3, 21, 87, 489, 2283, 11901, 58047, 294609, 1459923, 7338981, 36576807, 183238329, 915128763, 4578832461, 22884596367, 114451679649, 572172304803, 2861119804341, 14304824180727, 71526445426569, 357625253564043

Offset: 0

Author

Paul Barry, Apr 23 2003

Keywords

• easy
• nonn

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (2,15).

Crossrefs

Cf. A083232, A053524 (binomial transform, shifted).

Programs

Magma

[(3*5^n+(-3)^n)/4: n in [0..25]]; // Vincenzo Librandi, Jun 29 2011

Formula

a(n) = (3*5^n + (-3)^n)/4.

G.f.: (1+x)/((1-5*x)*(1+3*x)).

E.g.f.: (3*exp(5*x) + exp(-3*x))/4.