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 A302695 Number of 6-cycles in the (n+5)-path complement graph. 3
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS 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

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Last modified March 21 23:08 EDT 2023. Contains 361412 sequences. (Running on oeis4.)