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 A283329 a(n) = (1 + Sum_{j=1..K-1} a(n-j) + a(n-1)*a(n-K+1))/a(n-K) with a(1),...,a(K)=1, where K=4. 3
 1, 1, 1, 1, 5, 13, 33, 217, 617, 1633, 10813, 30805, 81601, 540401, 1539601, 4078401, 27009205, 76949213, 203838433, 1349919817, 3845921017, 10187843233, 67468981613, 192219101605, 509188323201, 3372099160801, 9607109159201, 25449228316801, 168537489058405 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,5 LINKS Seiichi Manyama, Table of n, a(n) for n = 1..1770 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; see also. Index entries for linear recurrences with constant coefficients, signature (0,0,51,0,0,-51,0,0,1). FORMULA From Seiichi Manyama, Mar 18 2017: (Start) a(3*n)   = 3*a(3*n-1) - a(3*n-2) - 1, a(3*n+1) = 3*a(3*n)   - a(3*n-1) - 1, a(3*n+2) = 7*a(3*n+1) - a(3*n)   - 1. (End) From Colin Barker, Nov 03 2020: (Start) G.f.: x*(1 + x + x^2 - 50*x^3 - 46*x^4 - 38*x^5 + 33*x^6 + 13*x^7 + 5*x^8) / ((1 - x)*(1 + x + x^2)*(1 - 50*x^3 + x^6)). a(n) = 51*a(n-3) - 51*a(n-6) + a(n-9). (End) PROG (Ruby) def A(k, n)   a = Array.new(k, 1)   ary = [1]   while ary.size < n     j = (1..k - 1).inject(1){|s, i| s + a[-i]} + a[1] * a[-1]     break if j % a[0] > 0     a = *a[1..-1], j / a[0]     ary << a[0]   end   ary end def A283329(n)   A(4, n) end # Seiichi Manyama, Mar 18 2017 CROSSREFS Cf. A276123, A283330. Sequence in context: A147086 A032406 A146917 * A201170 A106587 A034509 Adjacent sequences:  A283326 A283327 A283328 * A283330 A283331 A283332 KEYWORD nonn AUTHOR N. J. A. Sloane, Mar 17 2017 EXTENSIONS More terms from Seiichi Manyama, Mar 17 2017 STATUS approved

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Last modified January 26 23:54 EST 2022. Contains 350601 sequences. (Running on oeis4.)