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 A275176 a(n) = (3 * a(n-3) + a(n-1) * a(n-5)) / a(n-6), a(0) = a(1) = ... = a(5) = 1. 3
 1, 1, 1, 1, 1, 1, 4, 7, 10, 22, 43, 202, 370, 547, 1264, 2521, 11881, 21781, 32221, 74521, 148681, 700744, 1284667, 1900450, 4395442, 8769643, 41331982, 75773530, 112094287, 259256524, 517260241, 2437886161, 4469353561, 6611662441, 15291739441, 30509584561 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,7 COMMENTS Inspired by A048736. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,60,0,0,0,0,-60,0,0,0,0,1). FORMULA G.f.: (1 +x +x^2 +x^3 +x^4 -59*x^5 -56*x^6 -53*x^7 -50*x^8 -38*x^9 +43*x^10 +22*x^11 +10*x^12 +7*x^13 +4*x^14) / ((1 -x)*(1 +x +x^2 +x^3 +x^4)*(1 -59*x^5 +x^10)). - Colin Barker, Jul 19 2016 a(n) = 60*a(n-5) - 60*a(n-10) + a(n-15). MATHEMATICA RecurrenceTable[{a[n] == (3 a[n - 3] + a[n - 1] a[n - 5])/a[n - 6], a[1] == 1, a[2] == 1, a[3] == 1, a[4] == 1, a[5] == 1, a[6] == 1}, a, {n, 36}] (* Michael De Vlieger, Jul 19 2016 *) PROG (Ruby) def A(k, l, n)   a = Array.new(k * 2, 1)   ary = [1]   while ary.size < n + 1     break if (a[1] * a[-1] + a[k] * l) % a[0] > 0     a = *a[1..-1], (a[1] * a[-1] + a[k] * l) / a[0]     ary << a[0]   end   ary end def A275176(n)   A(3, 3, n) end (PARI) Vec((1 +x +x^2 +x^3 +x^4 -59*x^5 -56*x^6 -53*x^7 -50*x^8 -38*x^9 +43*x^10 +22*x^11 +10*x^12 +7*x^13 +4*x^14) / ((1 -x)*(1 +x +x^2 +x^3 +x^4)*(1 -59*x^5 +x^10)) + O(x^50)) \\ Colin Barker, Jul 19 2016 CROSSREFS Cf. A048736, A275173, A275175. Sequence in context: A161863 A102649 A084386 * A024726 A024948 A296309 Adjacent sequences:  A275173 A275174 A275175 * A275177 A275178 A275179 KEYWORD nonn,easy AUTHOR Seiichi Manyama, Jul 19 2016 STATUS approved

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Last modified June 20 05:01 EDT 2019. Contains 324229 sequences. (Running on oeis4.)