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, Connected Dominating Set.
Index entries for linear recurrences with constant coefficients, signature (53,209,376,-673,71,-4479,2120,-428,320,16).
FORMULA
G.f.: (5 + 16*x + 11*x^2 - 437*x^3 + 1856*x^4 - 1403*x^5 + 5308*x^6 - 2044*x^7 + 656*x^8 - 368*x^9)/(1 - 53*x - 209*x^2 - 376*x^3 + 673*x^4 - 71*x^5 + 4479*x^6 - 2120*x^7 + 428*x^8 - 320*x^9 - 16*x^10). - Andrew Howroyd, Aug 31 2025
a(n) = 53*a(n-1)+209*a(n-2)+376*a(n-3)-673*a(n-4)+71*a(n-5)-4479*a(n-6)+2120*a(n-7)-428*a(n-8)+320*a(n-9)+16*a(n-10). - Eric W. Weisstein, Sep 03 2025
MATHEMATICA
LinearRecurrence[{53, 209, 376, -673, 71, -4479, 2120, -428, 320, 16}, {281, 15949, 905469, 51427345, 2920698969, 165875085993, 9420532825569, 535019698383817, 30385338406252141, 1725672517842528533}, {0, 20}] (* Eric W. Weisstein, Sep 03 2025 *)
CoefficientList[Series[(-5 - 16 x - 11 x^2 + 437 x^3 - 1856 x^4 + 1403 x^5 - 5308 x^6 + 2044 x^7 - 656 x^8 + 368 x^9)/(-1 + 53 x + 209 x^2 + 376 x^3 - 673 x^4 + 71 x^5 - 4479 x^6 + 2120 x^7 - 428 x^8 + 320 x^9 + 16 x^10), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 03 2025 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Aug 28 2025
EXTENSIONS
a(0) prepended and a(4) onwards from Andrew Howroyd, Aug 31 2025
STATUS
approved