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0, 1, 6, 19, 60, 181, 546, 1639, 4920, 14761, 44286, 132859, 398580, 1195741, 3587226, 10761679, 32285040, 96855121, 290565366, 871696099, 2615088300, 7845264901, 23535794706, 70607384119, 211822152360, 635466457081
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| This is the sequence A(0,1;2,3;4) of the family of sequences [a,b:c,d:k] considered by G. Detlefs, and treated as A(a,b;c,d;k) in the W. Lang link given below. [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 18 2010]
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LINKS
| W. Lang, Notes on certain inhomogeneous three term recurrences. [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 18 2010]
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FORMULA
| a(n) = Sum{i=0..n, Sum{k=1..i, Binomial(i, 2k-2)2^(2k-2)}}
G.f.: x(1+3x)/((1+x)(1-x)(1-3x)); E.g.f.: (3exp(3x)+exp(-x))/4-exp(x); a(n)=(3*3^n+(-1)^n)/4-1.
a(n) = 3*a(n-1) + a(n-2) - 3*a(n-3), a(0)=0, a(1)=1, a(2)=6. Observation by G. Detlefs. See the W.lang comment and link. [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 18 2010]
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MAPLE
| a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]+3*a[n-2]+4 od: seq(a[n], n=0..33); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 14 2008]
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CROSSREFS
| Sequence in context: A027044 A057571 A125069 * A184189 A152098 A041673
Adjacent sequences: A080923 A080924 A080925 * A080927 A080928 A080929
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Feb 26 2003
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