OFFSET
1,1
COMMENTS
This cylinder is horizontal: a chessboard where it is supposed that rows 1 and 2n are in contact (number of columns = 4, number of rows = 2n).
LINKS
Indranil Ghosh, Table of n, a(n) for n = 1..2091
Index entries for linear recurrences with constant coefficients, signature (6,-10,3).
FORMULA
a(n) = 2*3^n + 2*((3+sqrt(5))/2)^n + 2*((3-sqrt(5))/2)^n.
Recurrence: a(n) = 3*a(n-3) - 10*a(n-2) + 6*a(n-1).
G.f.: -2*(3-12*x+10*x^2)/((-1+3*x)*(1-3*x+x^2)).
MATHEMATICA
Table[2*3^n+2*LucasL[2n], {n, 25}]
Drop[CoefficientList[Series[-2*(3 - 12*x + 10*x^2)/((-1 + 3*x)*(1 - 3*x + x^2)), {x, 0, 27}], x], 1] (* or *) LinearRecurrence[{6, -10, 3}, {12, 32, 90}, 27] (* Indranil Ghosh, Mar 05 2017 *)
PROG
(PARI) print(Vec(-2*(3 - 12*x + 10*x^2)/((-1 + 3*x)*(1 - 3*x + x^2)) + O(x^27))); \\ Indranil Ghosh, Mar 05 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vaclav Kotesovec, Aug 31 2011
STATUS
approved