A387374 Number of connected induced subgraphs in the n-Cameron graph.

421, 26564, 1702720, 109099373, 6990954434, 447974968976, 28705909073977, 1839453802307198, 117870864072599395, 7553079389820352025, 483995843414924904314, 31014102242764208453587, 1987361154050789198470410, 127348659835918245187985574, 8160409661298021681557603875

Offset

1,1

Links

Andrew Howroyd, Table of n, a(n) for n = 1..200

Eric Weisstein's World of Mathematics, Cameron Graph.

Eric Weisstein's World of Mathematics, Connected Graph.

Eric Weisstein's World of Mathematics, Vertex-Induced Subgraph.

Index entries for linear recurrences with constant coefficients, signature (68,-241,-666,651,-672,1775,4412,-10032,5170,-464).

Formula

G.f.: x*(421 - 2064*x - 2171*x^2 - 3277*x^3 - 29857*x^4 + 17625*x^5 + 17634*x^6 - 19513*x^7 + 13630*x^8 - 1400*x^9)/((1 - x)^2*(1 - 66*x + 108*x^2 + 948*x^3 + 1137*x^4 + 1998*x^5 + 1084*x^6 - 4242*x^7 + 464*x^8)). - Andrew Howroyd, Aug 31 2025

a(n) = 68*a(n-1)-241*a(n-2)-666*a(n-3)+651*a(n-4)-672*a(n-5)+1775*a(n-6)+4412*a(n-7)-10032*a(n-8)+5170*a(n-9)-464*a(n-10). - Eric W. Weisstein, Sep 03 2025

Mathematica

LinearRecurrence[{68, -241, -666, 651, -672, 1775, 4412, -10032, 5170, -464}, {421, 26564, 1702720, 109099373, 6990954434, 447974968976, 28705909073977, 1839453802307198, 117870864072599395, 7553079389820352025}, 20] (* Eric W. Weisstein, Sep 03 2025 *)
CoefficientList[Series[(421 - 2064 x - 2171 x^2 - 3277 x^3 - 29857 x^4 + 17625 x^5 + 17634 x^6 - 19513 x^7 + 13630 x^8 - 1400 x^9)/((1 - x)^2 (1 - 66 x + 108 x^2 + 948 x^3 + 1137 x^4 + 1998 x^5 + 1084 x^6 - 4242 x^7 + 464 x^8)), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 03 2025 *)

Crossrefs

Cf. A387373.

Sequence in context: A303414 A242149 A083193 * A340871 A303334 A109505

Adjacent sequences: A387371 A387372 A387373 * A387375 A387376 A387377

Keyword

nonn,easy

Author

Eric W. Weisstein, Aug 28 2025

Extensions

a(4) onwards from Andrew Howroyd, Aug 31 2025

Status

approved