A064750 -id:A064750 - cp's OEIS frontend

A064758 a(n) = n*12^n - 1.

11, 287, 5183, 82943, 1244159, 17915903, 250822655, 3439853567, 46438023167, 619173642239, 8173092077567, 106993205379071, 1390911669927935, 17974858503684095, 231105323618795519, 2958148142320582655, 37716388814587428863, 479219999055934390271, 6070119988041835610111, 76675199848949502443519

Offset: 1

N. J. A. Sloane, Oct 19 2001

Harry J. Smith, Table of n, a(n) for n = 1..150
Paul Leyland, Factors of Cullen and Woodall numbers.
Paul Leyland, Generalized Cullen and Woodall numbers.
Index entries for linear recurrences with constant coefficients, signature (25,-168,144).

Cf. for a(n) = n*k^n - 1: -A000012(k=0), A001477(k=1), A003261 (k=2), A060352 (k=3), A060416 (k=4), A064751 (k=5), A064752 (k=6), A064753 (k=7), A064754 (k=8), A064755 (k=9), A064756 (k=10), A064757 (k=11), this sequence (k=12).

Cf. A064750.

[n*12^n - 1: n in [1..30]]; // Vincenzo Librandi, Jun 21 2018

CoefficientList[Series[(11 + 12 x - 144 x^2) / ((1 - 12 x)^2 (1 - x)), {x, 0, 33}], x] (* Vincenzo Librandi, Jun 21 2018 *)

a(n) = { n*12^n - 1 } \\ Harry J. Smith, Sep 24 2009

G.f.: x*(11 + 12*x - 144*x^2)/((1 - 12*x)^2*(1 - x)). - Vincenzo Librandi, Jun 21 2018
From Elmo R. Oliveira, Sep 07 2024: (Start)
E.g.f.: 1 + exp(x)*(12*x*exp(11*x) - 1).
a(n) = 25*a(n-1) - 168*a(n-2) + 144*a(n-3) for n > 3.
a(n) = A064750(n) - 2. (End)

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

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, Oct 19 2001

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).

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.

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

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

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)

cp's OEIS Frontend

A064758 a(n) = n*12^n - 1.

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