A377770 -id:A377770 - cp's OEIS frontend

A290933 Number of edge covers in the n-sun graph.

198, 4900, 240312, 23395376, 4531118784, 1749027373184, 1347335578414080, 2073100143249356800, 6374782039282565480448, 39187907355886437009522688, 481684681120059363288611291136, 11839809344351753924631214042382336, 582001612807237989283840810619309654016

Offset: 3

Andrew Howroyd, Aug 14 2017

nonn

Eric Weisstein's World of Mathematics, Edge Cover.
Eric Weisstein's World of Mathematics, Sun Graph.

Cf. A192856, A290763, A377770.

a(8) onwards from Andrew Howroyd, Dec 12 2024

A378796 Number of minimal edge cuts in the n-sun graph.

Original entry on oeis.org

1, 6, 15, 44, 125, 370, 1099, 3288, 9849, 29534, 88583, 265732, 797173, 2391498, 7174467, 21523376, 64570097, 193710262, 581130751, 1743392220, 5230176621, 15690529826, 47071589435, 141214768264, 423644304745, 1270932914190, 3812798742519, 11438396227508, 34315188682469, 102945566047354

Offset: 1

Eric W. Weisstein, Dec 07 2024

The sequence has been extended to n=1 using the formula. - Andrew Howroyd, Dec 12 2024

Andrew Howroyd, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Minimal Edge Cut.
Eric Weisstein's World of Mathematics, Sun Graph.
Index entries for linear recurrences with constant coefficients, signature (4,-2,-4,3).

Cf. A046717, A377770.

Table[((-1)^n + 3^n + 2 n - 2)/2, {n, 20}]
LinearRecurrence[{4, -2, -4, 3}, {1, 6, 15, 44}, 20]
CoefficientList[Series[(-1 - 2 x + 7 x^2)/((-1 + x)^2 (-1 + 2 x + 3 x^2)), {x, 0, 20}], x]

a(n) = (3^n + (-1)^n)/2 + n - 1 \\ Andrew Howroyd, Dec 12 2024

a(n) = (3^n + (-1)^n)/2 + n - 1 = A046717(n) + n - 1. - Andrew Howroyd, Dec 12 2024
G.f.: x*(-1-2*x+7*x^2)/((-1+x)^2*(-1+2*x+3*x^2)). - Eric W. Weisstein, Dec 18 2024
E.g.f.: exp(x)*(cosh(2*x) - 1 + x). - Stefano Spezia, Dec 19 2024

a(1)-a(2) prepended and a(7) onwards from Andrew Howroyd, Dec 12 2024

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A290933 Number of edge covers in the n-sun graph.

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A378796 Number of minimal edge cuts in the n-sun graph.

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