A387433 Number of dominating sets in the n-Cameron graph.

15, 687, 123445, 22217385, 3998015863, 719448790681, 129465806292261, 23297551477617903, 4192426713354818233, 754433003972842510279, 135761265825306788853311, 24430428151245174661992773, 4396289442536280242818423199, 791118384946146380633498854261

Offset

0,1

Comments

The n-Cameron graph is defined for n >= 1. The sequence has been extended to a(0) using the recurrence. - Andrew Howroyd, Aug 31 2025

Links

Andrew Howroyd, Table of n, a(n) for n = 0..200

Eric Weisstein's World of Mathematics, Cameron Graph.

Eric Weisstein's World of Mathematics, Dominating Set.

Index entries for linear recurrences with constant coefficients, signature (171,1630,-3128,-60684,408220,1031036,1422260,896221,359221,94394,11884,948,452,100,4).

Formula

G.f.: (15 - 1878*x - 18482*x^2 + 35400*x^3 + 686874*x^4 - 4556874*x^5 - 11566900*x^6 - 16131486*x^7 - 10027805*x^8 - 4043804*x^9 - 1071150*x^10 - 156386*x^11 - 24612*x^12 - 5092*x^13 - 204*x^14)/(1 - 171*x - 1630*x^2 + 3128*x^3 + 60684*x^4 - 408220*x^5 - 1031036*x^6 - 1422260*x^7 - 896221*x^8 - 359221*x^9 - 94394*x^10 - 11884*x^11 - 948*x^12 - 452*x^13 - 100*x^14 - 4*x^15). - Andrew Howroyd, Aug 31 2025

a(n) = 171*a(n-1)+1630*a(n-2)-3128*a(n-3)-60684*a(n-4)+408220*a(n-5)+1031036*a(n-6)+1422260*a(n-7)+896221*a(n-8)+359221*a(n-9)+94394*a(n-10)+11884*a(n-11)+948*a(n-12)+452*a(n-13)+100*a(n-14)+4*a(n-15). - Eric W. Weisstein, Aug 31 2025

Mathematica

LinearRecurrence[{171, 1630, -3128, -60684, 408220, 1031036, 1422260, 896221, 359221, 94394, 11884, 948, 452, 100, 4}, {687, 123445, 22217385, 3998015863, 719448790681, 129465806292261, 23297551477617903, 4192426713354818233, 754433003972842510279, 135761265825306788853311, 24430428151245174661992773, 4396289442536280242818423199, 791118384946146380633498854261, 142362851031647945042577554446105, 25618392568691002593830067445166555}, {0, 20}] (* Eric W. Weisstein, Aug 31 2025 *)
CoefficientList[Series[(-15 + 1878 x + 18482 x^2 - 35400 x^3 - 686874 x^4 + 4556874 x^5 + 11566900 x^6 + 16131486 x^7 + 10027805 x^8 + 4043804 x^9 + 1071150 x^10 + 156386 x^11 + 24612 x^12 + 5092 x^13 + 204 x^14)/(-1 + 171 x + 1630 x^2 - 3128 x^3 - 60684 x^4 + 408220 x^5 + 1031036 x^6 + 1422260 x^7 + 896221 x^8 + 359221 x^9 + 94394 x^10 + 11884 x^11 + 948 x^12 + 452 x^13 + 100 x^14 + 4 x^15), {x, 0, 20}], x]  (* Eric W. Weisstein, Aug 31 2025 *)

Crossrefs

Cf. A387373.

Sequence in context: A351182 A266519 A177230 * A209499 A001520 A062079

Adjacent sequences: A387430 A387431 A387432 * A387434 A387435 A387436

Keyword

nonn,easy

Author

Eric W. Weisstein, Aug 29 2025

Extensions

a(0) prepended and a(4) onwards from Andrew Howroyd, Aug 31 2025

Status

approved