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A059633
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G.f.: x^3/(1 - 2*x + x^3 - x^4). Recurrence: a(n) = 2*a(n-1) - a(n-3) + a(n-4).
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7
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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
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OFFSET
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3,2
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LINKS
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Table of n, a(n) for n=3..34.
Index entries for linear recurrences with constant coefficients, signature (2,0,-1,1).
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FORMULA
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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
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MAPLE
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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
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CROSSREFS
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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
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KEYWORD
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nonn,easy
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AUTHOR
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James R. FitzSimons (cherry(AT)neta.com), Feb 19 2001
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EXTENSIONS
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Comments and more terms from Henry Bottomley, Feb 21 2001
New description from Vladeta Jovovic, Jan 17 2004
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STATUS
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approved
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