A158525 -id:A158525 - cp's OEIS frontend

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

Eric W. Weisstein, Nov 06 2024

nonn

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

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.

Cf. A158525.

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 *)

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

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

A377501 a(n) = 2 + 4^(n - 1) - (2 - sqrt(2))^(n - 1) - (2 + sqrt(2))^(n - 1).

Original entry on oeis.org

1, 2, 6, 26, 122, 562, 2514, 10978, 47074, 199106, 833346, 3459458, 14268290, 58542850, 239189250, 973889026, 3954048514, 16015899650, 64745436162, 261309683714, 1053186816002, 4239883710466, 17052184465410, 68525063462914, 275180257009666, 1104408389468162

Offset: 1

Eric W. Weisstein, Oct 30 2024

a(n) is also the number of edge cuts in the wheel graph on n vertices for n > 3.

Eric Weisstein's World of Mathematics, Edge Cut.
Eric Weisstein's World of Mathematics, Wheel Graph.
Index entries for linear recurrences with constant coefficients, signature (9,-26,26,-8).

Cf. A158525.

Table[2 + 4^(n - 1) - (2 - Sqrt[2])^(n - 1) - (2 + Sqrt[2])^(n - 1), {n, 26}]
LinearRecurrence[{9, -26, 26, -8}, {1, 2, 6, 26}, 20]
CoefficientList[Series[-(-1 + 7 x - 14 x^2 + 2 x^3)/((-1 + x) (-1 + 4 x) (1 - 4 x + 2 x^2)), {x, 0, 20}], x]

a(n) = 2 + 4^(n - 1) - (2 - sqrt(2))^(n - 1) - (2 + sqrt(2))^(n - 1) = 2+4^(n-1)-2*A006012(n-1).
a(n) = 9*a(n-1)-26*a(n-2)+26*a(n-3)-8*a(n-4).
G.f.: -x*(-1+7*x-14*x^2+2*x^3)/((-1+x)*(-1+4*x)*(1-4*x+2*x^2)).
a(n) = 2^(2*(n-1))-A158525(n) for n >= 4. - Pontus von Brömssen, Nov 06 2024
E.g.f.: exp(2*x)*(-2*cosh(sqrt(2)*x) - 2*sinh(x) + cosh(x)*(2 + sinh(x)) + sqrt(2)*sinh(sqrt(2)*x)). - Stefano Spezia, Nov 08 2024

cp's OEIS Frontend

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

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