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A212703 Main transitions in systems of n particles with spin 4. 9
8, 144, 1944, 23328, 262440, 2834352, 29760696, 306110016, 3099363912, 30993639120, 306837027288, 3012581722464, 29372671794024, 284688972772848, 2745215094595320, 26354064908115072, 252010745683850376, 2401514164751985936, 22814384565143866392 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Please, refer to the general explanation in A212697.

This sequence is for base b=9 (see formula), corresponding to spin S=(b-1)/2=4.

LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..100

Index entries for linear recurrences with constant coefficients, signature (18,-81).

FORMULA

a(n) = n*(b-1)*b^(n-1). For this sequence, set b=9.

a(n) = 18*a(n-1)-81*a(n-2). - Colin Barker, Jun 16 2015

G.f.: 8*x / (9*x-1)^2. - Colin Barker, Jun 16 2015

MATHEMATICA

LinearRecurrence[{18, -81}, {8, 144}, 30] (* Harvey P. Dale, Jun 28 2017 *)

PROG

(PARI): mtrans(n, b) = n*(b-1)*b^(n-1);

for (n=1, 100, write("b212703.txt", n, " ", mtrans(n, 9)))

(PARI) Vec(8*x/(9*x-1)^2 + O(x^100)) \\ Colin Barker, Jun 16 2015

(PARI) a(n)=8*n*9^(n-1) \\ Charles R Greathouse IV, Jun 16 2015

CROSSREFS

Cf. A001787, A212697, A212698, A212699, A212700, A212701, A212702, A212704 (b = 2, 3, 4, 5, 6, 7, 8, 10).

Sequence in context: A241229 A274730 A263604 * A065409 A061899 A134492

Adjacent sequences:  A212700 A212701 A212702 * A212704 A212705 A212706

KEYWORD

nonn,easy

AUTHOR

Stanislav Sykora, May 25 2012

STATUS

approved

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Last modified August 17 23:58 EDT 2017. Contains 290682 sequences.