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
Links
- Index entries for linear recurrences with constant coefficients, signature (12).
Programs
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Maple
a:= n-> ceil(11*12^(n-1)): seq(a(n), n=0..20); # Alois P. Heinz, Mar 25 2025
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Mathematica
Join[{1},NestList[12#&,11,20]] (* Harvey P. Dale, Sep 19 2018 *) -
PARI
a(n)=if(n,11*12^n--,1) \\ Charles R Greathouse IV, Oct 05 2011
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PARI
a(n)=(11+!n)*12^(n-1) \\ M. F. Hasler, Oct 05 2011
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)
Extensions
More terms from Elmo R. Oliveira, Mar 25 2025