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Search: id:A073371
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| A073371 |
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Convolution of A001045(n+1) (generalized (1,2)-Fibonacci), n>=0 with itself. |
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14
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| 1, 2, 7, 16, 41, 94, 219, 492, 1101, 2426, 5311, 11528, 24881, 53398, 114083, 242724, 514581, 1087410, 2291335, 4815680, 10097401, 21126862, 44117867, 91963996, 191384541, 397682154, 825190479, 1710033272, 3539371201, 7317351686
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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PSumSIGN transform of A045883(n-1). - Michael Somos, Jul 10 2003
Numbers of the form ((6n + 4)/27)2^(n) + ((-1)^(n - 1) )(3n + 4)/27. - Artur Jasinski (grafix(AT)csl.pl), Feb 09 2007
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REFERENCES
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Bosma W. 2001. Signed bits and fast exponentiation. J. Th. Nombres de Bordeaux Vol.13, Fasc. 1
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LINKS
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Bosma W. Signed bits and fast exponentiation.
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FORMULA
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a(n)=sum(b(k)*b(n-k), k=0..n) with b(k) := A001045(k+1).
a(n)=sum((n-k+1)*binomial(n-k, k)*2^k, k=0..floor(n/2)).
a(n)= ((n+1)*U(n+1)+2*2*(n+2)*U(n))/9 with U(n) := A001045(n+1), n>=0.
G.f.: 1/(1-(1+2*x)*x)^2.
G.f.: 1/((1+x)(1-2x))^2. a(n)=((5+3n)2^(n+2)+(7+3n)(-1)^n)/27.
a(n) = ((6n + 4)/27)2^(n) + ((-1)^(n - 1) )(3n + 4)/27 - Artur Jasinski (grafix(AT)csl.pl), Feb 09 2007
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MATHEMATICA
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Table[((6n + 4)/27)2^(n) + ((-1)^(n - 1) )(3n + 4)/27, {n, 1, 100}] - Artur Jasinski (grafix(AT)csl.pl), Feb 09 2007
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PROGRAM
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(PARI) a(n)=if(n<-3, 0, ((5+3*n)*2^(n+2)+(7+3*n)*(-1)^n)/27)
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CROSSREFS
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Second (m=1) column of triangle A073370.
Cf. A127976.
Adjacent sequences: A073368 A073369 A073370 this_sequence A073372 A073373 A073374
Sequence in context: A093971 A065497 A131727 this_sequence A113224 A026571 A100099
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Aug 2, 2002
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EXTENSIONS
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Edited by njas at the suggestion of Andrew Plewe, Jun 08 2007
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