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Search: id:A002534
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| A002534 |
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a(n) = 2a(n-1) + 9a(n-2).
(Formerly M2058 N0814)
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+0
9
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| 0, 1, 2, 13, 44, 205, 806, 3457, 14168, 59449, 246410, 1027861, 4273412, 17797573, 74055854, 308289865, 1283082416, 5340773617, 22229288978, 92525540509
(list; graph; listen)
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OFFSET
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0,3
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REFERENCES
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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.
A. Tarn, Approximations to certain square roots and the series of numbers connected therewith, Mathematical Questions and Solutions from the Educational Times, 1 (1916), 8-12.
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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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E.g.f. : exp(x)sinh(sqrt(10)x)/sqrt(10); a(n)=sum{k=0..n, binomial(n, 2k+1)10^k}. - Paul Barry (pbarry(AT)wit.ie), Sep 29 2004
a(n)=((1+sqrt(10))^n-(1-sqrt(10))^n)/(2Sqrt(10)) - Artur Jasinski (grafix(AT)csl.pl), Dec 10 2006
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MAPLE
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A002534:=-z/(-1+2*z+9*z**2); [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
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Table[((1 + Sqrt[10])^n - (1 - Sqrt[10])^n)/(2Sqrt[10]), {n, 0, 30}]] - Artur Jasinski (grafix(AT)csl.pl), Dec 10 2006
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CROSSREFS
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Sequence in context: A102296 A025194 A084156 this_sequence A117717 A005584 A072416
Adjacent sequences: A002531 A002532 A002533 this_sequence A002535 A002536 A002537
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KEYWORD
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nonn
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AUTHOR
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njas
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