The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A120756 Expansion of g.f. x*(1 +82*x +366*x^2 -189*x^3)/((1+3*x)*(1+9*x)*(1-21*x)). 1
 1, 91, 1410, 33543, 670734, 14383251, 299383290, 6310987263, 132315428934, 2780561320011, 58374353168370, 1226018323723383, 25744972644839934, 540657134887786371, 11353685448630220650, 238428423877048161903, 5006987636316607975734 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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). LINKS Nathaniel Johnston, Table of n, a(n) for n = 1..200 Index entries for linear recurrences with constant coefficients, signature (9,225,567). FORMULA 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) MATHEMATICA 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 *) PROG (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 CROSSREFS Sequence in context: A221815 A195221 A213559 * A027787 A333112 A140667 Adjacent sequences: A120753 A120754 A120755 * A120757 A120758 A120759 KEYWORD nonn,easy AUTHOR Gary W. Adamson and Roger L. Bagula, Jul 01 2006 EXTENSIONS Edited by N. J. A. Sloane, May 06 2010 Name changed by G. C. Greubel, Nov 14 2022 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 26 10:39 EDT 2023. Contains 361540 sequences. (Running on oeis4.)