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Search: id:A001610
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| A001610 |
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a(n) = a(n-1) + a(n-2) + 1.
(Formerly M0764 N0291)
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+0
11
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| 0, 2, 3, 6, 10, 17, 28, 46, 75, 122, 198, 321, 520, 842, 1363, 2206, 3570, 5777, 9348, 15126, 24475, 39602, 64078, 103681, 167760, 271442, 439203, 710646, 1149850, 1860497, 3010348, 4870846, 7881195, 12752042, 20633238, 33385281, 54018520
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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For prime p, p divides a(p-1). [From T. D. Noe (noe(AT)sspectra.com), Apr 11 2009]
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
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.
D. Jarden, Recurring Sequences. Riveon Lematematika, Jerusalem, 1966.
J. W. Wrench, Jr., Evaluation of Artin's constant and the twin-prime constant, Math. Comp., 15 (1961), 396-398.
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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) = A000204(n)-1 = A000032(n+1)-1 = A000071(n+1)+A000045(n)
a(n)=F(n)+F(n+2)-1 {where F(n) is the n-th Fibonacci number} - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008
a(n) = A014217(n+1)- A000035(n+1). - Paul Curtz (bpcrtz(AT)free.fr), Sep 21 2008
a(n)=-1+(1/2)*[1/2+(1/2)*sqrt(5)]^n+(1/2)*[1/2+(1/2)*sqrt(5)]^n*sqrt(5)-(1/2)*sqrt(5)*[1/2-(1/2) *sqrt(5)]^n+(1/2)*[1/2-(1/2)*sqrt(5)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Sep 29 2008]
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MAPLE
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A001610:=-z*(-2+z)/(z-1)/(z**2+z-1); [Conjectured by S. Plouffe in his 1992 dissertation.]
with(combinat): seq(fibonacci(n)+fibonacci(n+2)-1, n=0..36); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 31 2008
g:=(1+z^2)/(1-z-z^2): gser:=series(g, z=0, 43): seq(coeff(gser, z, n)-1, n=1..37); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 09 2009]
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CROSSREFS
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Cf. A001610, A000032, A000204.
Adjacent sequences: A001607 A001608 A001609 this_sequence A001611 A001612 A001613
Sequence in context: A026647 A026669 A023614 this_sequence A135431 A123908 A026397
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Henry Bottomley (se16(AT)btinternet.com), Jul 06 2000
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