A302695 Number of 6-cycles in the (n+5)-path complement graph.

0, 5, 50, 265, 996, 2985, 7610, 17185, 35320, 67341, 120770, 205865, 336220, 529425, 807786, 1199105, 1737520, 2464405, 3429330, 4691081, 6318740, 8392825, 11006490, 14266785, 18295976, 23232925, 29234530, 36477225, 45158540, 55498721, 67742410, 82160385, 99051360

Offset

0,2

Links

Table of n, a(n) for n=0..32.

Eric Weisstein's World of Mathematics, Graph Cycle

Eric Weisstein's World of Mathematics, Path Complement Graph

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

G.f.: x*(-5 - 15*x - 20*x^2 - 16*x^3 - 3*x^4 - x^5)/(-1 + x)^7.

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).

a(n) = n*(4 + 22*n + 17*n^2 + 13*n^3 + 3*n^4 + n^5)/12.

Mathematica

Table[n (4 + 22 n + 17 n^2 + 13 n^3 + 3 n^4 + n^5)/12, {n, 0, 20}]
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {5, 50, 265, 996, 2985, 7610, 17185}, {0, 20}]
CoefficientList[Series[x (-5 - 15 x - 20 x^2 - 16 x^3 - 3 x^4 - x^5)/(-1 + x)^7, {x, 0, 20}], x]

Prog

(PARI) a(n) = n*(4+22*n+17*n^2+13*n^3+3*n^4+n^5)/12; \\ Altug Alkan, Apr 12 2018

Crossrefs

Cf. A000292 (3-cycles of \bar P_{n+4}), A002817 (4-cycles of \bar P_{n+4}), A060446 (5-cycles of \bar P_{n+3}).

Sequence in context: A061160 A226548 A274064 * A064054 A301821 A301997

Adjacent sequences: A302692 A302693 A302694 * A302696 A302697 A302698

Keyword

nonn,easy

Author

Eric W. Weisstein, Apr 11 2018

Status

approved