A081033 6th binomial transform of the periodic sequence (1,7,1,1,7,1...).

1, 13, 121, 997, 7729, 57853, 423721, 3059797, 21887329, 155555053, 1100604121, 7762822597, 54632726929, 383893932253, 2694581744521, 18898693305397, 132473958606529, 928233237589453, 6502210299844921, 45538360282508197, 318882962895526129, 2232752944858526653

Offset: 0

Author

Paul Barry, Mar 03 2003

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (12,-35).

Crossrefs

Cf. A080134, A080962.

Programs

Magma

[4*7^n-3*5^n: n in [0..25]]; // Vincenzo Librandi, Aug 06 2013

Mathematica

CoefficientList[Series[(1 + x) / ((1 - 5 x) (1 - 7 x)),{x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)
LinearRecurrence[{12,-35},{1,13},30] (* Harvey P. Dale, Aug 18 2015 *)

Formula

a(n) = 7*a(n-1) + 6*5^(n-1).

a(n) = 4*7^n - 3*5^n.

G.f.: (1+x)/((1-5*x)*(1-7*x)). - Vincenzo Librandi, Aug 06 2013

E.g.f.: exp(5*x)*(4*exp(2*x) - 3). - Stefano Spezia, Jul 23 2024