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A006499 Number of restricted circular combinations.
(Formerly M2768)
2
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; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Table of n, a(n) for n=0..35.

G. E. Bergum and V. E. Hoggatt, Jr., A combinatorial problem involving recursive sequences and tridiagonal matrices, Fib. Quart., 16 (1978), 113-118.

T. Guardia, D. Jiménez, Fiboquadratic Sequences and Extensions of the Cassini Identity Raised From the Study of Rithmomachia, arXiv preprint arXiv:1509.03177 [math.HO], 2015-2016.

Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992.

Simon Plouffe, 1031 Generating Functions and Conjectures, Université du Québec à Montréal, 1992.

Index entries for linear recurrences with constant coefficients, signature (1,0,1,1).

FORMULA

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

MAPLE

A006499:=-(1+2*z+6*z**2+2*z**3)/((z**2+z-1)*(1+z**2)); # [Conjectured (correctly) by Simon Plouffe in his 1992 dissertation.]

MATHEMATICA

CoefficientList[ Series[(1 + 2x + 6x^2 + 2x^3)/((1 + x^2)(1 - x - x^2)), {x, 0, 35}], x] (* Robert G. Wilson v, Feb 25 2005 *)

CROSSREFS

Equals A000032(n+2) - 2*A056594(n) - A056594(n-1).

Sequence in context: A244147 A103531 A108860 * A310320 A274676 A310321

Adjacent sequences:  A006496 A006497 A006498 * A006500 A006501 A006502

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified October 23 13:07 EDT 2018. Contains 316528 sequences. (Running on oeis4.)