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A099099
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Quadrisection of a generalized Padovan sequence.
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1
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1, 1, 1, 2, 6, 16, 37, 80, 172, 377, 839, 1874, 4175, 9274, 20577, 45665, 101393, 225193, 500162, 1110790, 2466760, 5477917, 12164896, 27015092, 59993817, 133231279, 295872778, 657057431, 1459155634, 3240410561, 7196122817
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OFFSET
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0,4
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COMMENTS
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Quadrisection of sequence with g.f. 1/(1-x^3-x^4), or A017817.
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LINKS
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Table of n, a(n) for n=0..30.
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FORMULA
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G.f.: (1-x)^3/((1-x)^4-x^3); a(n)=sum{k=0..2n, binomial(k, 4n-3k)}; a(n)=4a(n-1)-6a(n-2)+5a(n-3)-a(n-4); a(n)=A017817(4n).
a(n)=sum{k=0..floor((n+1)/2), binomial(n+k, 4k)} - Paul Barry, May 09 2005
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MATHEMATICA
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Join[{1}, a=0; b=0; c=0; d=1; Table[a+=b; b+=c; c+=d; d+=a, {n, 50}]] [From Vladimir Joseph Stephan Orlovsky, Nov 19 2010]
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CROSSREFS
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Sequence in context: A066641 A026540 A128232 * A074082 A212383 A097813
Adjacent sequences: A099096 A099097 A099098 * A099100 A099101 A099102
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry, Sep 29 2004
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STATUS
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approved
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