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 A276123 a(0) = a(1) = a(2) = 1; for n > 2, a(n) = (a(n-1) + 1)*(a(n-2) + 1) / a(n-3). 6
 1, 1, 1, 4, 10, 55, 154, 868, 2449, 13825, 39025, 220324, 621946, 3511351, 9912106, 55961284, 157971745, 891869185, 2517635809, 14213945668, 40124201194, 226531261495, 639469583290, 3610286238244, 10191389131441, 57538048550401, 162422756519761 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Matthew Christopher Russell, Using experimental mathematics to conjecture and prove theorems in the theory of partitions and commutative and non-commutative recurrences", PhD Dissertation, Mathematics Department, Rutgers University, May 2016. Index entries for linear recurrences with constant coefficients, signature (0,17,0,-17,0,1). FORMULA a(n) = (9-3*(-1)^n)/2*a(n-1) - a(n-2) - 1. From Colin Barker, Aug 21 2016: (Start) a(n) = 17*a(n-2) - 17*a(n-4) + a(n-6) for n > 5. G.f.: (1 + x - 16*x^2 - 13*x^3 + 10*x^4 + 4*x^5) / ((1-x)*(1+x)*(1 - 16*x^2 + x^4)). (End) MATHEMATICA LinearRecurrence[{0, 17, 0, -17, 0, 1}, {1, 1, 1, 4, 10, 55}, 40] (* Vincenzo Librandi, Aug 27 2016 *) nxt[{a_, b_, c_}]:={b, c, ((c+1)(b+1))/a}; NestList[nxt, {1, 1, 1}, 30][[All, 1]] (* Harvey P. Dale, Oct 01 2021 *) PROG (PARI) Vec((1+x-16*x^2-13*x^3+10*x^4+4*x^5)/((1-x)*(1+x)*(1-16*x^2+x^4)) + O(x^30)) \\ Colin Barker, Aug 21 2016 (Magma) I:=[1, 1, 1, 4, 10, 55]; [n le 6 select I[n] else 17*Self(n-2)-17*Self(n-4)+Self(n-6): n in [1..30]]; // Vincenzo Librandi, Aug 27 2016 CROSSREFS Cf. A072881, A076839, A276175. Sequence in context: A007027 A192444 A197902 * A096423 A276130 A263044 Adjacent sequences: A276120 A276121 A276122 * A276124 A276125 A276126 KEYWORD nonn,easy AUTHOR Bruno Langlois, Aug 21 2016 EXTENSIONS More terms from Colin Barker, Aug 21 2016 STATUS approved

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Last modified June 1 02:11 EDT 2023. Contains 363068 sequences. (Running on oeis4.)