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 A212702 Main transitions in systems of n particles with spin 7/2. 8
 7, 112, 1344, 14336, 143360, 1376256, 12845056, 117440512, 1056964608, 9395240960, 82678120448, 721554505728, 6253472382976, 53876069761024, 461794883665920, 3940649673949184, 33495522228568064, 283726776524341248, 2395915001761103872, 20176126330619822080 (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=8 (see formula), corresponding to spin S=(b-1)/2=7/2. LINKS Stanislav Sykora, Table of n, a(n) for n = 1..100 Index entries for linear recurrences with constant coefficients, signature (16,-64). FORMULA a(n) = n*(b-1)*b^(n-1). For this sequence, set b=8. a(n) = 16*a(n-1)-64*a(n-2). - Colin Barker, Jun 16 2015 G.f.: 7*x / (8*x-1)^2. Colin Barker, Jun 16 2015 MATHEMATICA LinearRecurrence[{16, -64}, {7, 112}, 30] (* Harvey P. Dale, Feb 11 2016 *) PROG (PARI): mtrans(n, b) = n*(b-1)*b^(n-1); for (n=1, 100, write("b212702.txt", n, " ", mtrans(n, 8))) (PARI) Vec(7*x/(8*x-1)^2 + O(x^100)) \\ Colin Barker, Jun 16 2015 CROSSREFS Cf. A001787, A212697, A212698, A212699, A212700, A212701, A212703, A212704 (b = 2, 3, 4, 5, 6, 7, 9, 10). Sequence in context: A117795 A163700 A094219 * A217223 A067404 A129030 Adjacent sequences:  A212699 A212700 A212701 * A212703 A212704 A212705 KEYWORD nonn,easy AUTHOR Stanislav Sykora, May 25 2012 STATUS approved

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