A052934 -id:A052934 - cp's OEIS frontend

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

Philippe Deléham, Oct 05 2011

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

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

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

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

a(n)=if(n,11*12^n--,1) \\ Charles R Greathouse IV, Oct 05 2011

a(n)=(11+!n)*12^(n-1)  \\ M. F. Hasler, Oct 05 2011

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)

More terms from Elmo R. Oliveira, Mar 25 2025

A055846 a(n) = 25*6^(n-2), with a(0)=1 and a(1)=4.

Original entry on oeis.org

1, 4, 25, 150, 900, 5400, 32400, 194400, 1166400, 6998400, 41990400, 251942400, 1511654400, 9069926400, 54419558400, 326517350400, 1959104102400, 11754624614400, 70527747686400, 423166486118400, 2538998916710400

Offset: 0

Barry E. Williams, Jun 03 2000

For n>=2, a(n) is equal to the number of functions f:{1,2,...,n}->{1,2,3,4,5,6} such that for fixed, different x_1, x_2 in {1,2,...,n} and fixed y_1, y_2 in {1,2,3,4,5,6} we have f(x_1)<>y_1 and f(x_2)<> y_2. - Milan Janjic, Apr 19 2007

a(n) is the number of generalized compositions of n when there are 5*i-1 different types of i, (i=1,2,...). - Milan Janjic, Aug 26 2010

A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Index entries for linear recurrences with constant coefficients, signature (6)

First differences of A052934. Cf. A000400.

LinearRecurrence[{6},{1,4,25},30] (* Harvey P. Dale, May 25 2023 *)

a(n) = 25*6^(n-2), a(0)=1, a(1)=4. a(n) = 6a(n-1) + ((-1)^n)*binomial(2, 2-n); g.f.(x)=(1-x)^2/(1-6x).

a(n) = Sum_{k, 0<=k<=n} A201780(n,k)*4^k. - Philippe Deléham, Dec 05 2011

More terms from James Sellers, Jun 05 2000

cp's OEIS Frontend

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

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