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URL: https://oeis.org/A289162

⇱ A289162 - OEIS

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A289162
Number of 4-cycles in the n X n black bishop graph.
4
0, 0, 0, 6, 39, 106, 321, 644, 1402, 2412, 4382, 6842, 11097, 16198, 24311, 33768, 47908, 64056, 87084, 112974, 148539, 188034, 240669, 298540, 373758, 455780, 560170, 673218, 814541, 966686, 1153971, 1354576, 1598216, 1858032, 2169880, 2501142, 2894607, 3311130
OFFSET
1,4
LINKS
Eric Weisstein's World of Mathematics, Black Bishop Graph
Eric Weisstein's World of Mathematics, Graph Cycle
FORMULA
a(n) = ((-1 + n)*(15 - 193*n + 162*n^2 - 68*n^3 + 12*n^4 - 15*(-1)^n*(1 - 7*n + 2*n^2)))/240.
a(n) = 2*a(n-1)+3*a(n-2)-8*a(n-3)-2*a(n-4)+12*a(n-5)-2*a(n-6)-8*a(n-7)+3*a(n-8)+2*a(n-9)-a(n-10).
G.f.: x^4*(6 + 27*x + 10*x^2 + 40*x^3 + 8*x^4 + 5*x^5) / ((1 - x)^6*(1 + x)^4). - Colin Barker, Jun 27 2017
MATHEMATICA
Table[(n - 1) (15 - 193 n + 162 n^2 - 68 n^3 + 12 n^4 - 15 (-1)^n (2 n^2 - 7 n + 1))/240, {n, 20}]
LinearRecurrence[{2, 3, -8, -2, 12, -2, -8, 3, 2, -1}, {0, 0, 0, 6, 39, 106, 321, 644, 1402, 2412}, 20]
PROG
(PARI) concat(vector(3), Vec(x^4*(6 + 27*x + 10*x^2 + 40*x^3 + 8*x^4 + 5*x^5) / ((1 - x)^6*(1 + x)^4) + O(x^40))) \\ Colin Barker, Jun 27 2017
CROSSREFS
Cf. A289161 (3-cycles), A289163 (5-cycles), A289160 (6-cycles).
Sequence in context: A354728 A220855 A351047 * A164081 A164082 A159571
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Jun 26 2017
STATUS
approved