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%I #32 Sep 08 2022 08:45:01
%S 1,10,121,1452,17424,209088,2509056,30108672,361304064,4335648768,
%T 52027785216,624333422592,7492001071104,89904012853248,
%U 1078848154238976,12946177850867712,155354134210412544
%N a(n) = 121*12^(n-2), a(0)=1, a(1)=10.
%C 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
%C 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
%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
%H Vincenzo Librandi, <a href="/A056116/b056116.txt">Table of n, a(n) for n = 0..200</a>
%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</a>
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (12).
%F a(n) = 12*a(n-1) + (-1)^n*C(2, 2-n).
%F G.f.: (1-x)^2/(1-12*x).
%F a(n) = Sum_{k=0..n} A201780(n,k)*10^k. - _Philippe Deléham_, Dec 05 2011
%F E.g.f.: (23 - 12*x + 121*exp(12*x))/144. - _G. C. Greubel_, Jan 18 2020
%p 1,10, seq( 121*12^(n-2), n=2..20); # _G. C. Greubel_, Jan 18 2020
%t LinearRecurrence[{12},{1,10,121},20] (* _Harvey P. Dale_, Oct 20 2015 *)
%o (PARI) concat([1, 10], vector(20, n, 121*12^(n-1) )) \\ _G. C. Greubel_, Jan 18 2020
%o (Magma) [1,10] cat [121*12^(n-2): n in [2..20]]; // _G. C. Greubel_, Jan 18 2020
%o (Sage) [1,10]+[121*12^(n-2) for n in (2..20)] # _G. C. Greubel_, Jan 18 2020
%o (GAP) concatenation([1,10], List([2..20], n-> 121*12^(n-2) )); # _G. C. Greubel_, Jan 18 2020
%Y Cf. A055996, A056002.
%K nonn,easy
%O 0,2
%A _Barry E. Williams_, Jul 04 2000
%E More terms from _James A. Sellers_, Jul 04 2000
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