|
%I #17 Sep 08 2022 08:45:01
%S 1,1,7,27,108,432,1728,6912,27648,110592,442368,1769472,7077888,
%T 28311552,113246208,452984832,1811939328,7247757312,28991029248,
%U 115964116992,463856467968,1855425871872
%N a(n) = (3^3)*4^(n-3) with a(0)=1, a(1)=1 and a(2)=7.
%C For n>=3, a(n) is equal to the number of functions f:{1,2,...,n}->{1,2,3,4} such that for fixed, different x_1, x_2, x_3 in {1,2,...,n} and fixed y_1, y_2, y_3 in {1,2,3,4} we have f(x_i)<>y_i, (i=1,2,...,n). - _Milan Janjic_, May 13 2007
%H G. C. Greubel, <a href="/A056120/b056120.txt">Table of n, a(n) for n = 0..1000</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 (4).
%F a(n) = 4*a(n-1) + (-1)^n*binomial(3, 3-n).
%F G.f.: (1-x)^3/(1-4*x).
%F E.g.f.: (37 - 44*x + 8*x^2 + 27*exp(4*x))/64. - _G. C. Greubel_, Jan 18 2020
%p 1,1,7, seq( 27*4^(n-3), n=3..25); # _G. C. Greubel_, Jan 18 2020
%t Table[If[n<2, 1, If[n==2, 7, 27*4^(n-3)]], {n,0,25}] (* _G. C. Greubel_, Jan 18 2020 *)
%o (PARI) vector(26, n, if(n<2, 1, if(n==2, 7, 27*4^(n-3))) ) \\ _G. C. Greubel_, Jan 18 2020
%o (Magma) [1,1,7] cat [27*4^(n-3): n in [3..25]]; // _G. C. Greubel_, Jan 18 2020
%o (Sage) [1,1,7]+[27*4^(n-3) for n in (3..25)] # _G. C. Greubel_, Jan 18 2020
%o (GAP) Concatenation([1,1,7], List([3..25], n-> 27*4^(n-3) )); # _G. C. Greubel_, Jan 18 2020
%Y Cf. A055841.
%Y First differences of A002063.
%K easy,nonn
%O 0,3
%A _Barry E. Williams_, Jul 05 2000
%E a(21) corrected by _R. J. Mathar_, Dec 03 2014
|
