OFFSET
1,1
COMMENTS
Vertical cylinder: a chessboard where it is supposed that the columns 1 and 12 are in contact (number of columns = 12, number of rows = 2n).
LINKS
Ray Chandler, Table of n, a(n) for n = 1..3296
V. Kotesovec, Non-attacking chess pieces
Index entries for linear recurrences with constant coefficients, signature (9, -34, 70, -85, 61, -24, 4).
FORMULA
Recurrence: a(n) = 4*a(n-7) - 24*a(n-6) + 61*a(n-5) - 85*a(n-4) + 70*a(n-3) - 34*a(n-2) + 9*a(n-1).
G.f.: -(1 + 119*x + 984*x^2 + 1352*x^3 + 307*x^4 + 9*x^5)/((x-1)^5*(2*x-1)^2).
a(n) = (15839*n - 99729)*2^n + 231/2*n^4 + 1767*n^3 + 26001/2*n^2 + 53295*n + 99730.
MATHEMATICA
LinearRecurrence[{9, -34, 70, -85, 61, -24, 4}, {128, 2102, 15988, 81606, 327192, 1118398, 3419648}, 30] (* Harvey P. Dale, Aug 06 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Sep 21 2011
STATUS
approved