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A289705 Number of 4-cycles in the n-triangular honeycomb queen graph. 3
0, 0, 15, 96, 330, 855, 1866, 3624, 6468, 10818, 17193, 26208, 38598, 55209, 77028, 105168, 140904, 185652, 241011, 308736, 390786, 489291, 606606, 745272, 908076, 1098006, 1318317, 1572480, 1864254, 2197629, 2576904, 3006624, 3491664, 4037160, 4648599, 5331744, 6092730 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..37.

Eric Weisstein's World of Mathematics, Graph Cycle

Index entries for linear recurrences with constant coefficients, signature (4, -4, -4, 10, -4, -4, 4, -1).

FORMULA

a(n) = (24*n^5 + 170*n^4 - 660*n^3 + 160*n^2 + 606*n - 165 + (-1)^n*(165 - 30*n))/320.

a(n) = 4*a(n-1)-4*a(n-2)-4*a(n-3)+10*a(n-4)-4*a(n-5)-4*a(n-6)+4*a(n-7)-a(n-8).

G.f.: (-3*x^3*(-5 - 12*x - 2*x^2 + 7*x^3))/((-1 + x)^6*(1 + x)^2).

MATHEMATICA

Table[(24 n^5 + 170 n^4 - 660 n^3 + 160 n^2 + 606 n - 165 + (-1)^n (165 - 30 n))/320, {n, 20}]

LinearRecurrence[{4, -4, -4, 10, -4, -4, 4, -1}, {0, 0, 15, 96, 330, 855, 1866, 3624}, 20]

CoefficientList[Series[-((3 x^2 (-5 - 12 x - 2 x^2 + 7 x^3))/((-1 + x)^6 (1 + x)^2)), {x, 0, 20}], x]

CROSSREFS

Cf. A105636 (3-cycles), A289706 (5-cycles), A289707 (6-cycles).

Sequence in context: A336278 A044266 A044647 * A296538 A298105 A283168

Adjacent sequences:  A289702 A289703 A289704 * A289706 A289707 A289708

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Jul 14 2017

STATUS

approved

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Last modified April 22 14:33 EDT 2021. Contains 343177 sequences. (Running on oeis4.)