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Search: id:A006499
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| A006499 |
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Number of restricted circular combinations.
(Formerly M2768)
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+0
2
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| 1, 3, 9, 12, 16, 28, 49, 77, 121, 198, 324, 522, 841, 1363, 2209, 3572, 5776, 9348, 15129, 24477, 39601, 64078, 103684, 167762, 271441, 439203, 710649, 1149852, 1860496, 3010348, 4870849, 7881197, 12752041, 20633238, 33385284, 54018522
(list; graph; listen)
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OFFSET
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0,2
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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).
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.
G. E. Bergum and V. E. Hoggatt, Jr., A combinatorial problem involving recursive sequences and tridiagonal matrices, Fib. Quart., 16 (1978), 113-118.
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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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G.f.: [1+2x+6x^2+2x^3]/[(1+x^2)(1-x-x^2)]. - Ralf Stephan, Apr 23 2004
Lucas(n+2) - I^n - (-I)^n - 1/2*I^(n-1) - 1/2*(-I)^(n-1). - Ralf Stephan, Jun 09 2005
(1/2) {Lucas(n+2) - 3(-1)^[n/2] + (-1)^[(n-1)/2] }. - Ralf Stephan, Jun 09 2005
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MAPLE
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A006499:=-(1+2*z+6*z**2+2*z**3)/(z**2+z-1)/(1+z**2); [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
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CoefficientList[ Series[(1 + 2x + 6x^2 + 2x^3)/((1 + x^2)(1 - x - x^2)), {x, 0, 35}], x] (from Robert G. Wilson v Feb 25 2005)
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CROSSREFS
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Equals A000032(n+2) - 2*A056594(n) - A056594(n-1).
Sequence in context: A136290 A103531 A108860 this_sequence A140979 A096726 A155504
Adjacent sequences: A006496 A006497 A006498 this_sequence A006500 A006501 A006502
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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 Robert G. Wilson v (rgwv(AT)rgwv.com), Feb 25 2005
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