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Search: id:A006138
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| A006138 |
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a(n)=a(n-1)+3a(n-2).
(Formerly M1399)
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+0
4
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| 1, 2, 5, 11, 26, 59, 137, 314, 725, 1667, 3842, 8843, 20369, 46898, 108005, 248699, 572714, 1318811, 3036953, 6993386, 16104245, 37084403, 85397138, 196650347, 452841761
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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The binomial transform of a(n) is b(n)=A006190(n+1), which satisfies b(n)=3b(n-1)+b(n-2). - Paul Barry (pbarry(AT)wit.ie), May 21 2006
Partial sums of A105476. - Paul Barry (pbarry(AT)wit.ie), Feb 02 2007
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REFERENCES
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N. T. Gridgeman, A new look at Fibonacci generalization, Fib,. Quart., 11 (1973), 40-55.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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a(n)=Sum_{k, 0<=k<=n+1}A122950(n+1,k)*2^(n+1-k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 04 2008
G.f.: (1+x)/(1-x-3x^2); - Paul Barry (pbarry(AT)wit.ie), May 21 2006
a(n)=sum{k=0..n, C(floor((2n-k)/2),n-k)*3^floor(k/2)} - Paul Barry (pbarry(AT)wit.ie), Feb 02 2007
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MAPLE
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A006138:=-(1+z)/(-1+z+3*z**2); [S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Sequence in context: A005469 A026787 A064416 this_sequence A124217 A095981 A082397
Adjacent sequences: A006135 A006136 A006137 this_sequence A006139 A006140 A006141
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KEYWORD
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nonn
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AUTHOR
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njas
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