A196791 a(n) = A047848(9, n).

1, 2, 14, 158, 1886, 22622, 271454, 3257438, 39089246, 469070942, 5628851294, 67546215518, 810554586206, 9726655034462, 116719860413534, 1400638324962398, 16807659899548766, 201691918794585182, 2420303025535022174, 29043636306420266078, 348523635677043192926

Offset: 0

Author

Vincenzo Librandi, Oct 11 2011

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..900
• Index entries for linear recurrences with constant coefficients, signature (13,-12).

Crossrefs

Cf. A047848, A047849, A047850, A047851, A047852, A047853, A047854, A047855, A047856.

Cf. A001021 (first differences).

Programs

Magma

[(12^n+10)/11: n in [0..20]];

Mathematica

LinearRecurrence[{13,-12},{1,2},30] (* Harvey P. Dale, Sep 07 2015 *)
(12^Range[0,40] +10)/11 (* G. C. Greubel, Jan 17 2025 *)

Python

def A196791(n): return (pow(12, n) + 10)//11
print([A196791(n) for n in range(41)]) # G. C. Greubel, Jan 17 2025

Formula

a(n) = (12^n + 10)/11.

a(n) = 12*a(n-1) - 10, with a(0) = 1.

G.f.: (1-11*x)/((1-x)*(1-12*x)). - Bruno Berselli, Oct 11 2011

From Elmo R. Oliveira, Aug 30 2024: (Start)

E.g.f.: exp(x)*(exp(11*x) + 10)/11.

a(n) = 13*a(n-1) - 12*a(n-2) for n > 1. (End)