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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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3
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,2
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
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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).
n>=2 a(n+1)=sum(i=0, n, F(i)*binomial(n-i, i)) where F=A000045 - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 21 2004
a(n)=sum{k=0..n+1, C(k+1, n-k+1)F(n-k+1)} [offset 0] - Paul Barry (pbarry(AT)wit.ie), Feb 23 2005
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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); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 04 2009]
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CROSSREFS
| I and J are A049856 while K and L are A059633 (with some offsets).
Sequence in context: A160254 A005318 A102111 * A088353 A192654 A018184
Adjacent sequences: A059630 A059631 A059632 * A059634 A059635 A059636
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KEYWORD
| nonn
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AUTHOR
| James R. FitzSimons (cherry(AT)neta.com), Feb 19 2001
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EXTENSIONS
| Comments and more terms from Henry Bottomley (se16(AT)btinternet.com), Feb 21 2001
New description from Vladeta Jovovic (vladeta(AT)eunet.rs), Jan 17 2004
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