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

Author

Eric W. Weisstein, Nov 06 2024

Keywords

• nonn

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.

Crossrefs

Cf. A158525.

Programs

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 *)

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

Extensions

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