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

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

Author

Eric W. Weisstein, Dec 07 2024

Keywords

• nonn
• easy

Comments

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

Links

• 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).

Crossrefs

Cf. A046717, A377770.

Programs

Mathematica

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]

PARI

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

Formula

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

Extensions

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