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 A059633 G.f.: x^3/(1 - 2*x + x^3 - x^4). Recurrence: a(n) = 2*a(n-1) - a(n-3) + a(n-4). 8
 1, 2, 4, 7, 13, 24, 45, 84, 157, 293, 547, 1021, 1906, 3558, 6642, 12399, 23146, 43208, 80659, 150571, 281080, 524709, 979506, 1828503, 3413377, 6371957, 11894917, 22204960, 41451340, 77379720, 144449397, 269652414 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,2 LINKS Index entries for linear recurrences with constant coefficients, signature (2,0,-1,1). FORMULA Recurrence equations (A059633 is L(n)): I(n + 1) = I(n) + J(n) + L(n); J(n + 1) = I(n); K(n + 1) = J(n) + K(n); L(n + 1) = K(n); M(n + 1) = L(n) + 2M(n); initial conditions: I(0) = 1; J(0) = 0; K(0) = 0; L(0) = 0; M(0) = 0. Values for n = 0 1 2 3 4 5 6 7 8 ...: I(n) = 1 1 2 3 6 11 21 39 73 ... J(n) = 0 1 1 2 3 6 11 21 39 ... K(n) = 0 0 1 2 4 7 13 24 45 ... L(n) = 0 0 0 1 2 4 7 13 24 ... M(n) = 0 0 0 0 1 4 12 31 75 ... a(n) = A049856(n+2) - A049856(n+1) - A049856(n) + A049856(n-1). For n >= 2, a(n+1) = Sum_{i=0..n} Fibonacci(i)*binomial(n-i, i). - Benoit Cloitre, Sep 21 2004 a(n) = Sum_{k=0..n+1} C(k+1, n-k+1)F(n-k+1) [offset 0]. - Paul Barry, Feb 23 2005 MAPLE with(combstruct): SeqSeqSeqL := [T, {T=Sequence(S), S=Sequence(U, card > 1), U=Sequence(Z, card >1)}, unlabeled]: seq(count(SeqSeqSeqL, size=j), j=4..35); # Zerinvary Lajos, Apr 04 2009 CROSSREFS I and J are A049856 while K and L are A059633 (with some offsets). Sequence in context: A102111 A224704 A265826 * A088353 A192654 A260668 Adjacent sequences:  A059630 A059631 A059632 * A059634 A059635 A059636 KEYWORD nonn,easy AUTHOR James R. FitzSimons (cherry(AT)neta.com), Feb 19 2001 EXTENSIONS Comments and more terms from Henry Bottomley, Feb 21 2001 New description from Vladeta Jovovic, Jan 17 2004 STATUS approved

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Last modified August 1 09:36 EDT 2021. Contains 346385 sequences. (Running on oeis4.)