A196731 Expansion of g.f. (1-x)/(1-12*x).

1, 11, 132, 1584, 19008, 228096, 2737152, 32845824, 394149888, 4729798656, 56757583872, 681091006464, 8173092077568, 98077104930816, 1176925259169792, 14123103110037504, 169477237320450048, 2033726847845400576, 24404722174144806912, 292856666089737682944, 3514279993076852195328

Offset

0,2

Links

Table of n, a(n) for n=0..20.

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

Formula

a(n) = Sum_{k=0..n} A193722(n,k)*9^(n-k).

a(n+1) = 12*a(n) for n > 0. - M. F. Hasler, Oct 05 2011

From Elmo R. Oliveira, Mar 18 2025: (Start)

a(n) = 11*12^(n-1) with a(0)=1.

E.g.f.: (11*exp(12*x) + 1)/12. (End)

Maple

a:= n-> ceil(11*12^(n-1)):
seq(a(n), n=0..20);  # Alois P. Heinz, Mar 25 2025

Mathematica

Join[{1}, NestList[12#&, 11, 20]] (* Harvey P. Dale, Sep 19 2018 *)

Prog

(PARI) a(n)=if(n, 11*12^n--, 1) \\ Charles R Greathouse IV, Oct 05 2011
(PARI) a(n)=(11+!n)*12^(n-1)  \\ M. F. Hasler, Oct 05 2011

Crossrefs

Cf. A002001, A005054, A025192, A052934, A055272, A055274, A055276, A193722.

Sequence in context: A229252 A242163 A105280 * A289415 A051431 A014994

Adjacent sequences: A196728 A196729 A196730 * A196732 A196733 A196734

Keyword

nonn,easy

Author

Philippe Deléham, Oct 05 2011

Extensions

More terms from Elmo R. Oliveira, Mar 25 2025

Status

approved