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

1,2

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).

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

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]

Prog

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

Crossrefs

Cf. A046717, A377770.

Sequence in context: A272320 A137806 A193449 * A197160 A182420 A117961

Adjacent sequences: A378793 A378794 A378795 * A378797 A378798 A378799

Keyword

nonn,easy

Author

Eric W. Weisstein, Dec 07 2024

Extensions

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

Status

approved