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A078042 Expansion of (1-x)/(1+x-x^2+x^3). 29
1, -2, 3, -6, 11, -20, 37, -68, 125, -230, 423, -778, 1431, -2632, 4841, -8904, 16377, -30122, 55403, -101902, 187427, -344732, 634061, -1166220, 2145013, -3945294, 7256527, -13346834, 24548655, -45152016, 83047505, -152748176, 280947697, -516743378, 950439251, -1748130326, 3215312955 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Absolute values give coordination sequence for (3,infinity,infinity) tiling of hyperbolic plane. - N. J. A. Sloane, Dec 29 2015

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

J. W. Cannon, P. Wagreich, Growth functions of surface groups, Mathematische Annalen, 1992, Volume 293, pp. 239-257. See Prop. 3.1.

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

FORMULA

a(0)=1, a(1)=-2, a(2)=3; for n>2, a(n) = -a(n-1)+a(n-2)-a(n-3). - Harvey P. Dale, Jun 01 2012

a(n) = (-1)^n * A001590(n+2).

MATHEMATICA

CoefficientList[Series[(1-x)/(1+x-x^2+x^3), {x, 0, 40}], x] (* or *) LinearRecurrence[{-1, 1, -1}, {1, -2, 3}, 40] (* Harvey P. Dale, Jun 01 2012 *)

PROG

(PARI) Vec((1-x)/(1+x-x^2+x^3)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

(MAGMA) [n le 3 select -n*(-1)^n else -Self(n-1)+Self(n-2)-Self(n-3): n in [1..50]]; // Vincenzo Librandi, Dec 30 2015

CROSSREFS

Coordination sequences for triangular tilings of hyperbolic space: A001630, A007283, A054886, A078042, A096231, A163876, A179070, A265057, A265058, A265059, A265060, A265061, A265062, A265063, A265064, A265065, A265066, A265067, A265068, A265069, A265070, A265071, A265072, A265073, A265074, A265075, A265076, A265077.

Sequence in context: A065615 A054182 A001590 * A115792 A054177 A186546

Adjacent sequences:  A078039 A078040 A078041 * A078043 A078044 A078045

KEYWORD

sign,easy

AUTHOR

N. J. A. Sloane, Nov 17 2002

STATUS

approved

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Last modified November 14 03:52 EST 2018. Contains 317159 sequences. (Running on oeis4.)