OFFSET
0,2
COMMENTS
Also, coordination sequence for (6,6,6) tiling of hyperbolic plane. - N. J. A. Sloane, Dec 29 2015
The initial terms coincide with those of A003945, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
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, 1, 1, -1).
FORMULA
G.f.: (x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1)/(x^6 - x^5 - x^4 - x^3 - x^2 - x + 1).
G.f.: (1+x)*(1-x^6)/(1-2*x+2*x^6-x^7). - G. C. Greubel, Apr 25 2019
a(n) = -a(n-6) + Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 07 2021
MATHEMATICA
coxG[{6, 1, -1, 40}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 22 2015 *)
CoefficientList[Series[(1+x)*(1-x^6)/(1-2*x+2*x^6-x^7), {x, 0, 40}], x] (* G. C. Greubel, Aug 06 2017, modified Apr 25 2019 *)
PROG
(PARI) x='x+O('x^40); Vec((x^6+2*x^5+2*x^4+2*x^3+2*x^2+2*x+1)/(x^6-x^5- x^4-x^3-x^2-x+1)) \\ G. C. Greubel, Aug 06 2017
(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^6)/(1-2*x+2*x^6-x^7) )); // G. C. Greubel, Apr 25 2019
(Sage) ((1+x)*(1-x^6)/(1-2*x+2*x^6-x^7)).series(x, 40).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019
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.
KEYWORD
nonn,easy
AUTHOR
John Cannon and N. J. A. Sloane, Dec 03 2009
STATUS
approved