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A220838 Tropical version of Somos-4 sequence A006720. 3
-1, 0, 0, 0, 1, 1, 2, 3, 3, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 22, 25, 27, 30, 33, 35, 39, 42, 45, 49, 52, 56, 60, 63, 68, 72, 76, 81, 85, 90, 95, 99, 105, 110, 115, 121, 126, 132, 138, 143, 150, 156, 162, 169, 175, 182, 189, 195, 203, 210, 217, 225, 232 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,7

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000

A. Fordy and A. Hone, Discrete integrable systems and Poisson algebras from cluster maps, arXiv:1207.6072 [nlin.SI], 2012, See Example 3.6.

A. P. Fordy, Periodic Cluster Mutations and Related Integrable Maps, arXiv preprint arXiv:1403.8061 [math-ph], 2014.

Index entries for linear recurrences with constant coefficients, signature (2,-1,0,0,0,0,0,1,-2,1).

FORMULA

From Michael Somos, Dec 27 2012: (Start)

G.f.: x * (x^6 - x^5 + x^4 - x^2 + 2*x - 1) / ( (1 - x)^2 * (1 - x^8) ).

a(2-n) = a(n). (End)

Second difference has period 8. - Michael Somos, Dec 27 2012

EXAMPLE

G.f. = -x + x^5 + x^6 + 2*x^7 + 3*x^8 + 3*x^9 + 5*x^10 + 6*x^11 + 7*x^12 + ...

MAPLE

A118825x := proc(n)

    coeftayl((1-2*x+x^2)/(x^4+1), x=0, n) ;

end proc:

A056594 := proc(n)

    coeftayl(1/(x^2+1), x=0, n) ;

end proc:

A220838 := proc(n)

    -9/32-1/8*n+1/16*n^2+1/32*(-1)^n ;

    %+A118825x(n)/4 - A056594(n+3)/8  ;

end proc:

seq(A220838(n), n=0..80) ; # R. J. Mathar, Jan 30 2013

MATHEMATICA

LinearRecurrence[{2, -1, 0, 0, 0, 0, 0, 1, -2, 1}, {-1, 0, 0, 0, 1, 1, 2, 3, 3, 5}, 62] (* Jean-Fran├žois Alcover, Nov 26 2017 *)

PROG

(PARI) {a(n) = if( n<1, n = 2-n); polcoeff( x * (x^6 - x^5 + x^4 - x^2 + 2*x - 1) / ( (1 - x)^2 * (1 - x^8) ) + x * O(x^n), n)} /* Michael Somos, Dec 27 2012 */

(MAGMA) m:=25; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*( x^6-x^5+x^4-x^2+2*x-1)/((1-x)^2*(1-x^8)))); // G. C. Greubel, Aug 10 2018

CROSSREFS

Sequence in context: A070321 A239904 A334819 * A236294 A251419 A036410

Adjacent sequences:  A220835 A220836 A220837 * A220839 A220840 A220841

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Dec 23 2012

STATUS

approved

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Last modified June 5 23:10 EDT 2020. Contains 334858 sequences. (Running on oeis4.)