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A120756
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Expansion of g.f. x*(1 +82*x +366*x^2 -189*x^3)/((1+3*x)*(1+9*x)*(1-21*x)).
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1
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1, 91, 1410, 33543, 670734, 14383251, 299383290, 6310987263, 132315428934, 2780561320011, 58374353168370, 1226018323723383, 25744972644839934, 540657134887786371, 11353685448630220650, 238428423877048161903, 5006987636316607975734
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OFFSET
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1,2
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COMMENTS
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Former name: a(n) = leftmost term of M^n * [1,0,0,0,0,0] where M is the 6 X 6 matrix [1,2,3,4,5,6; 2,3,1,5,6,4; 3,1,2,6,4,5; 4,6,5,1,3,2; 5,4,6,2,1,3; 6,5,4,3,2,1].
M is a multiplication table for the symmetric group of degree 3 (S_3).
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LINKS
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Nathaniel Johnston, Table of n, a(n) for n = 1..200
Index entries for linear recurrences with constant coefficients, signature (9,225,567).
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FORMULA
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G.f.: x*(1 +82*x +366*x^2 -189*x^3)/((1+3*x)*(1+9*x)*(1-21*x)). - Colin Barker, Dec 13 2012
From G. C. Greubel, Nov 14 2022: (Start)
a(n) = (9*(21)^n + 9*(-9)^n + 24*(-3)^n + 18*[n=1] - 42*[n=0])/54.
E.g.f.: (1/54)*(-42 + 18*x + 24*exp(-3*x) + 9*exp(-9*x) + 9*exp(21*x)). (End)
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MATHEMATICA
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LinearRecurrence[{9, 225, 567}, {1, 91, 1410, 33543}, 20] (* Harvey P. Dale, Apr 11 2018 *)
M= {{1, 2, 3, 4, 5, 6}, {2, 3, 1, 5, 6, 4}, {3, 1, 2, 6, 4, 5}, {4, 6, 5, 1, 3, 2}, {5, 4, 6, 2, 1, 3}, {6, 5, 4, 3, 2, 1}};
A120756[n_]:= A120756[n]= MatrixPower[M, n][[1, 1]];
Table[A120756[n], {n, 30}] (* G. C. Greubel, Nov 14 2022 *)
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PROG
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(Magma) I:=[91, 1410, 33543]; [1] cat [n le 3 select I[n] else 9*Self(n-1) + 225*Self(n-2) +567*Self(n-3): n in [1..31]]; // G. C. Greubel, Nov 14 2022
(SageMath)
def A120756(n): return (9*(21)^n +9*(-9)^n +24*(-3)^n +18*int(n==1) -42*int(n==0))/54
[A120756(n) for n in range(1, 30)] # G. C. Greubel, Nov 14 2022
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CROSSREFS
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Sequence in context: A221815 A195221 A213559 * A027787 A333112 A140667
Adjacent sequences: A120753 A120754 A120755 * A120757 A120758 A120759
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KEYWORD
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nonn,easy
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AUTHOR
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Gary W. Adamson and Roger L. Bagula, Jul 01 2006
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EXTENSIONS
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Edited by N. J. A. Sloane, May 06 2010
Name changed by G. C. Greubel, Nov 14 2022
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STATUS
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approved
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