A056116 a(n) = 121*12^(n-2), a(0)=1, a(1)=10.

1, 10, 121, 1452, 17424, 209088, 2509056, 30108672, 361304064, 4335648768, 52027785216, 624333422592, 7492001071104, 89904012853248, 1078848154238976, 12946177850867712, 155354134210412544

Offset

0,2

Comments

For n >= 2, a(n) is equal to the number of functions f:{1,2,...,n}->{1,2,3,4,5,6,7,8,9,10,11,12} such that for fixed, different x_1, x_2 in {1,2,...,n} and fixed y_1, y_2 in {1,2,3,4,5,6,7,8,9,10,11,12} 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 11*i-1 different types of i, (i=1,2,...). - Milan Janjic, Aug 26 2010

References

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

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

Formula

a(n) = 12*a(n-1) + (-1)^n*C(2, 2-n).

G.f.: (1-x)^2/(1-12*x).

a(n) = Sum_{k=0..n} A201780(n,k)*10^k. - Philippe Deléham, Dec 05 2011

E.g.f.: (23 - 12*x + 121*exp(12*x))/144. - G. C. Greubel, Jan 18 2020

Maple

1, 10, seq( 121*12^(n-2), n=2..20); # G. C. Greubel, Jan 18 2020

Mathematica

LinearRecurrence[{12}, {1, 10, 121}, 20] (* Harvey P. Dale, Oct 20 2015 *)

Prog

(PARI) concat([1, 10], vector(20, n, 121*12^(n-1) )) \\ G. C. Greubel, Jan 18 2020
(Magma) [1, 10] cat [121*12^(n-2): n in [2..20]]; // G. C. Greubel, Jan 18 2020
(Sage) [1, 10]+[121*12^(n-2) for n in (2..20)] # G. C. Greubel, Jan 18 2020
(GAP) concatenation([1, 10], List([2..20], n-> 121*12^(n-2) )); # G. C. Greubel, Jan 18 2020

Crossrefs

Cf. A055996, A056002.

Sequence in context: A202808 A091692 A098309 * A246643 A233084 A081784

Adjacent sequences: A056113 A056114 A056115 * A056117 A056118 A056119

Keyword

nonn,easy

Author

Barry E. Williams, Jul 04 2000

Extensions

More terms from James A. Sellers, Jul 04 2000

Status

approved