|
|
A289179
|
|
Edge count of the n X n white bishop graph.
|
|
1
|
|
|
0, 1, 4, 14, 28, 55, 88, 140, 200, 285, 380, 506, 644, 819, 1008, 1240, 1488, 1785, 2100, 2470, 2860, 3311, 3784, 4324, 4888, 5525, 6188, 6930, 7700, 8555, 9440, 10416, 11424, 12529, 13668, 14910, 16188, 17575, 19000, 20540, 22120, 23821, 25564, 27434, 29348, 31395
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,3
|
|
COMMENTS
|
Sequence extended to a(1) using formula.
|
|
LINKS
|
|
|
FORMULA
|
a(n) = ((-1 + n)*(-3 + 3*(-1)^n - 2*n + 4*n^2))/12.
a(n) = 2*a(n-1)+a(n-2)-4*a(n-3)+a(n-4)+2*a(n-5)-a(n-6).
G.f. = x*(x + 2x^2 + 5x^3)/((-1 + x)^4*(1 + x)^2). [Corrected by Georg Fischer, May 19 2019]
|
|
MATHEMATICA
|
Table[(n - 1) (4 n^2 - 2 n - 3 + 3 (-1)^n)/12, {n, 20}]
LinearRecurrence[{2, 1, -4, 1, 2, -1}, {0, 1, 4, 14, 28, 55}, 20]
CoefficientList[Series[x(x + 2 x^2+ 5 x^3)/((-1 + x)^4 (1 + x)^2), {x, 0, 20}], x] (* Corrected by Georg Fischer, May 19 2019 *)
|
|
CROSSREFS
|
Cf. A225972 (black bishop graph edge count).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|