A047856 a(n) = A047848(8, n).

1, 2, 13, 134, 1465, 16106, 177157, 1948718, 21435889, 235794770, 2593742461, 28531167062, 313842837673, 3452271214394, 37974983358325, 417724816941566, 4594972986357217, 50544702849929378, 555991731349223149, 6115909044841454630, 67274999493256000921, 740024994425816010122

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• easy

Comments

n-th difference of a(n), a(n-1), ..., a(0) is A011557(n-1) for n >= 1.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..955
• Index entries for linear recurrences with constant coefficients, signature (12,-11).

Crossrefs

Cf. A011557, A047848.

Programs

Magma

[(11^n +9)/10: n in [0..40]]; // G. C. Greubel, Jan 12 2025

Maple

a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=11*a[n-1]+1 od: seq(a[n]+1, n=0..16); # Zerinvary Lajos, Mar 20 2008

Mathematica

(11^Range[0,40] +9)/10 (* G. C. Greubel, Jan 12 2025 *)

Python

def A047856(n): return (pow(11, n) + 9)//10
print([A047856(n) for n in range(41)]) # G. C. Greubel, Jan 12 2025

Formula

a(n) = (11^n + 9)/10. - Ralf Stephan, Feb 14 2004

From Philippe Deléham, Oct 06 2009: (Start)

a(0) = 1, a(1) = 2, a(n) = 12*a(n-1) - 11*a(n-2) for n > 1.

G.f.: (1 - 10*x)/(1 - 12*x + 11*x^2). (End)

a(n) = 11*a(n-1) - 9, with a(0)=1. - Vincenzo Librandi, Aug 06 2010

E.g.f.: exp(x)*(exp(10*x) + 9)/10. - Elmo R. Oliveira, Aug 30 2024

Extensions

a(17)-a(21) from Elmo R. Oliveira, Aug 30 2024