A377759 Number of edge cuts in the n-double cone graph.

1, 12, 156, 2652, 47580, 835132, 14274492, 239210620, 3954121852, 64745687292, 1053187674876, 17052187400700, 275180267037180, 4430223031522300, 71202253472533500, 1142950923338418172, 18330518457789188092, 293793080103272648700, 4706573484385846964220

Offset

0,2

Comments

Extended to a(0) using the formula/recurrence. - Eric W. Weisstein, Dec 01 2024

Links

Christian Sievers, Table of n, a(n) for n = 0..830

Index entries for linear recurrences with constant coefficients, signature (35,-408,1898,-3980,3880,-1680,256).

Eric Weisstein's World of Mathematics, Double Cone Graph.

Eric Weisstein's World of Mathematics, Edge Cut.

Formula

a(n) = 16^n - A158525(n+1)^2. - Christian Sievers, Nov 21 2024

G.f.: -(1-23*x+144*x^2+190*x^3-388*x^4-360*x^5+16*x^6)/((-1+x)*(-1+2*x)*(-1+16*x)*(1-4*x+2*x^2)*(1-12*x+4*x^2)). - Eric W. Weisstein, Dec 01 2024

a(n) = 35*a(n-1)-408*a(n-2)+1898*a(n-3)-3980*a(n-4)+3880*a(n-5)-1680*a(n-6)+256*a(n-7). - Eric W. Weisstein, Dec 01 2024

Mathematica

Table[16^n - 4 - 2^(n + 1) + -2^n ((3 + 2 Sqrt[2])^n + (3 - 2 Sqrt[2])^n) + 4 ((2 - Sqrt[2])^n + (2 + Sqrt[2])^n), {n, 0, 20}] // Expand (* Eric W. Weisstein, Dec 01 2024 *)
Table[16^n - 4 - 2^(n + 1) (ChebyshevT[n, 3] + 1) + 4 ((2 - Sqrt[2])^n + (2 + Sqrt[2])^n), {n, 0, 20}] // Expand (* Eric W. Weisstein, Dec 01 2024 *)
LinearRecurrence[{35, -408, 1898, -3980, 3880, -1680, 256}, {1, 12, 156, 2652, 47580, 835132, 14274492}, 20] (* Eric W. Weisstein, Dec 01 2024 *)
CoefficientList[Series[-(1 - 23 x + 144 x^2 + 190 x^3 - 388 x^4 - 360 x^5 + 16 x^6)/((-1 + x) (-1 + 2 x) (-1 + 16 x) (1 - 4 x + 2 x^2) (1 - 12 x + 4 x^2)), {x, 0, 20}], x] (* Eric W. Weisstein, Dec 01 2024 *)

Crossrefs

Cf. A158525.

Sequence in context: A110216 A218839 A036276 * A003130 A015000 A220225

Adjacent sequences: A377756 A377757 A377758 * A377760 A377761 A377762

Keyword

nonn,changed

Author

Eric W. Weisstein, Nov 06 2024

Extensions

a(7) and beyond from Christian Sievers, Nov 21 2024

Status

approved