A064749 a(n) = n*11^n + 1.

1, 12, 243, 3994, 58565, 805256, 10629367, 136410198, 1714871049, 21221529220, 259374246011, 3138428376722, 37661140520653, 448795257871104, 5316497670165375, 62658722541234766, 735195677817154577, 8592599484487994108, 100078511642860166659, 1162022718519876379530

Offset: 0

Author

N. J. A. Sloane, Oct 19 2001

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..900
• Paul Leyland, Factors of Cullen and Woodall numbers.
• Paul Leyland, Generalized Cullen and Woodall numbers.
• Index entries for linear recurrences with constant coefficients, signature (23,-143,121).

Crossrefs

For a(n)=n*k^n+1: A000012 (k=0), A000027(n+1) (k=1), A002064 (k=2), A050914 (k=3), A050915 (k=4), A050916 (k=5), A050917 (k=6), A050919 (k=7), A064746 (k=8), A064747 (k=9), A064748 (k=10), this sequence (k=11), A064750 (k=12).

Cf. A064757.

Programs

Magma

[n*11^n+1: n in [0..20]]; // Vincenzo Librandi, Sep 16 2011

Maple

k:= 11; f:= gfun:-rectoproc({-1 - (k-1)*n + k*n*a(n-1) - (n-1)*a(n) = 0, a(0) = 1, a(1) = k+1}, a(n), remember): map(f, [$0..20]); # Georg Fischer, Feb 19 2021

Formula

a(n) = A064757(n) + 2 for n>=1. - Georg Fischer, Feb 19 2021

G.f.: -(110*x^2-11*x+1)/((x-1)*(11*x-1)^2). - Alois P. Heinz, Feb 19 2021

From Elmo R. Oliveira, May 03 2025: (Start)

E.g.f.: exp(x)*(1 + 11*x*exp(10*x)).

a(n) = 23*a(n-1) - 143*a(n-2) + 121*a(n-3). (End)