A377500 Number of edge cuts in the n-dipyramidal graph.

1, 6, 32, 198, 1440, 11606, 98288, 847622, 7330624, 63161910, 540889232, 4601341542, 38896557792, 326918917526, 2733694633520, 22756578640838, 188690303469184, 1559143587993846, 12843876796018640, 105519766294576422, 864831673532666400, 7072996102954328150

Offset

0,2

Comments

The sequence has been extended to n=0 using the recurrence. - Andrew Howroyd, Nov 26 2024

Links

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

Eric Weisstein's World of Mathematics, Dipyramidal Graph.

Eric Weisstein's World of Mathematics, Edge Cut.

Index entries for linear recurrences with constant coefficients, signature (24,-215,896,-1808,1760,-784,128).

Formula

G.f.: (1 - 18*x + 103*x^2 - 176*x^3 + 32*x^5 + 16*x^6)/((1 - x)*(1 - 2*x)*(1 - 8*x)*(1 - 5*x + 2*x^2)*(1 - 8*x + 4*x^2)). - Andrew Howroyd, Nov 26 2024

a(n) = 24*a(n-1)-215*a(n-2)+896*a(n-3)-1808*a(n-4)+1760*a(n-5)-784*a(n-6)+128*a(n-7). - Eric W. Weisstein, Dec 01 2024

Mathematica

Table[8^n - 1 - 2^n ((2 - Sqrt[3])^n + (2 + Sqrt[3])^n - 1) + (1/2 (5 - Sqrt[17]))^n + (1/2 (5 + Sqrt[17]))^n, {n, 0, 20}] // Expand (* Eric W. Weisstein, Dec 01 2024 *)
LinearRecurrence[{24, -215, 896, -1808, 1760, -784, 128}, {1, 6, 32, 198, 1440, 11606, 98288}, 20] (* Eric W. Weisstein, Dec 01 2024 *)
CoefficientList[Series[-(1 - 18 x + 103 x^2 - 176 x^3 + 32 x^5 + 16 x^6)/((-1 + x) (-1 + 2 x) (-1 + 8 x) (1 - 5 x + 2 x^2) (1 - 8 x + 4 x^2)), {x, 0, 20}], x] (* Eric W. Weisstein, Dec 01 2024 *)

Prog

(PARI) Vec((1 - 18*x + 103*x^2 - 176*x^3 + 32*x^5 + 16*x^6)/((1 - x)*(1 - 2*x)*(1 - 8*x)*(1 - 5*x + 2*x^2)*(1 - 8*x + 4*x^2)) + O(x^25)) \\ Andrew Howroyd, Nov 26 2024

Crossrefs

Cf. A296995.

Sequence in context: A319228 A216441 A108188 * A020058 A146557 A020013

Adjacent sequences: A377497 A377498 A377499 * A377501 A377502 A377503

Keyword

nonn,easy

Author

Eric W. Weisstein, Oct 30 2024

Extensions

a(0)-a(2) prepended and a(10) onwards from Andrew Howroyd, Nov 26 2024

Status

approved