A377773 Number of edge cuts in the n-web graph.

1, 12, 223, 3898, 64453, 1042868, 16747743, 268285422, 4294211881, 68715706984, 1099492954547, 17592094126818, 281474526684989, 4503597434338652, 72057583394694855, 1152921453139596758, 18446743825630274641, 295147903987017778256, 4722366477153821698011

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
• Eric Weisstein's World of Mathematics, Edge Cut.
• Eric Weisstein's World of Mathematics, Web Graph.
• Index entries for linear recurrences with constant coefficients, signature (28,-242,888,-1481,1196,-452,64).

Crossrefs

Cf. A359621.

Programs

Magma

I:=[1, 12, 223, 3898, 64453, 1042868, 16747743]; [n le 7 select I[n] else 28*Self(n-1)-242*Self(n-2)+888*Self(n-3)-1481*Self(n-4)+1196*Self(n-5)-452*Self(n-6)+64*Self(n-7): n in [1..40]]; // Vincenzo Librandi, Jan 02 2025

Mathematica

LinearRecurrence[{28, -242, 888, -1481, 1196, -452, 64}, {1, 12, 223, 3898, 64453, 1042868, 16747743}, 20] (* Eric W. Weisstein, Dec 01 2024 *)
CoefficientList[Series[-(1 - 16 x + 129 x^2 - 330 x^3 + 100 x^4 + 52 x^5 + 4 x^6)/((-1 + x)^2 (-1 + 16 x) (1 - 5 x + 2 x^2)^2), {x, 0, 20}], x] (* Eric W. Weisstein, Dec 01 2024 *)

Formula

a(n) = 16^n - 8^n + A359621(n). - Christian Sievers, Nov 21 2024

a(n) = 28*a(n-1)-242*a(n-2)+888*a(n-3)-1481*a(n-4)+1196*a(n-5)-452*a(n-6)+64*a(n-7). - Eric W. Weisstein, Dec 01 2024

G.f.: -(1-16*x+129*x^2-330*x^3+100*x^4+52*x^5+4*x^6)/((-1+x)^2*(-1+16*x)*(1-5*x+2*x^2)^2). - Eric W. Weisstein, Dec 01 2024

Extensions

a(8) and beyond from Christian Sievers, Nov 21 2024