A024140 a(n) = 12^n - 1.

0, 11, 143, 1727, 20735, 248831, 2985983, 35831807, 429981695, 5159780351, 61917364223, 743008370687, 8916100448255, 106993205379071, 1283918464548863, 15407021574586367, 184884258895036415

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

In base 12 these are 0, B, BB, BBB, ... . - David Rabahy, Dec 12 2016

Links

• Index entries for linear recurrences with constant coefficients, signature (13,-12).

Crossrefs

Cf. A001021, A016125, A178248.

Cf. Similar sequences of the type k^n-1: A000004 (k=1), A000225 (k=2), A024023 (k=3), A024036 (k=4), A024049 (k=5), A024062 (k=6), A024075 (k=7), A024088 (k=8), A024101 (k=9), A002283 (k=10), A024127 (k=11), this sequence (k=12).

Programs

Mathematica

12^Range[0,20]-1 (* or *) LinearRecurrence[{13,-12},{0,11},20] (* Harvey P. Dale, Feb 01 2019 *)

Formula

From Mohammad K. Azarian, Jan 14 2009: (Start)

G.f.: 1/(1-12*x) - 1/(1-x).

E.g.f.: exp(12*x) - exp(x). (End)

a(n) = 12*a(n-1) + 11 for n>0, a(0)=0. - Vincenzo Librandi, Nov 18 2010

a(n) = Sum_{i=1..n} 11^i*binomial(n,n-i) for n>0, a(0)=0. - Bruno Berselli, Nov 11 2015

From Elmo R. Oliveira, Dec 15 2023: (Start)

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

a(n) = A001021(n)-1 = A178248(n)-2.

a(n) = 11*(A016125(n) - 1)/12. (End)