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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). 7
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

Table of n, a(n) for n=3..34.

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 October 17 16:08 EDT 2017. Contains 293471 sequences.