A378924 Number of minimal edge cuts in the n-Plummer-Toft graph.

12, 22, 38, 65, 113, 202, 372, 703, 1355, 2648, 5222, 10357, 20613, 41110, 82088, 164027, 327887, 655588, 1310970, 2621713, 5243177, 10486082, 20971868, 41943415, 83886483, 167772592, 335544782, 671089133, 1342177805, 2684355118, 5368709712, 10737418867

Offset

0,1

Comments

The sequence has been extended to n=0 using the formula. - Andrew Howroyd, Dec 11 2024

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Eric Weisstein's World of Mathematics, Minimal Edge Cut.

Eric Weisstein's World of Mathematics, Plummer-Toft Graph.

Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).

Formula

From Andrew Howroyd, Dec 11 2024: (Start)

a(n) = 5*2^n + (n+2)*(n+7)/2.

G.f.: (12 - 38*x + 36*x^2 - 11*x^3)/((1 - x)^3*(1 - 2*x)). (End)

Mathematica

Table[5 2^n + n (9 + n)/2 + 7, {n, 0, 20}]
LinearRecurrence[{5, -9, 7, -2}, {22, 38, 65, 113}, {0, 20}]
CoefficientList[Series[x (22 - 72 x + 73 x^2 - 24 x^3)/((-1 + x)^3 (-1 + 2 x)), {x, 0, 20}], x]

Prog

(PARI) a(n) = (n+2)*(n+7)/2 + 5*2^n \\ Andrew Howroyd, Dec 11 2024

Crossrefs

Cf. A377769.

Sequence in context: A124885 A115745 A375084 * A129639 A153361 A200197

Adjacent sequences: A378921 A378922 A378923 * A378925 A378926 A378927

Keyword

nonn,easy

Author

Eric W. Weisstein, Dec 11 2024

Extensions

a(0)=12 prepended and a(8) onwards from Andrew Howroyd, Dec 11 2024

Status

approved