login
A301758
Clique covering number of the n X n fiveleaper graph.
1
1, 4, 9, 16, 21, 22, 25, 32, 41, 50, 61, 72, 85, 98, 113, 128, 145, 162, 181, 200, 221, 242, 265, 288, 313, 338, 365, 392, 421, 450, 481, 512, 545, 578, 613, 648, 685, 722, 761, 800, 841, 882, 925, 968, 1013, 1058, 1105, 1152, 1201, 1250, 1301, 1352, 1405
OFFSET
1,2
LINKS
Eric Weisstein's World of Mathematics, Clique Covering Number.
Eric Weisstein's World of Mathematics, Fiveleaper Graph.
FORMULA
a(n) = (3-(-1)^n + 2*(n-1)*(n+1))/4 for n > 6.
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4) for n >= 10.
G.f.: x*(-1 - 2*x - x^2 + 4*x^4 + 6*x^5 - 4*x^6 - 8*x^7 + 4*x^9)/((-1 +
x)^3*(1 + x)).
MATHEMATICA
Join[{1, 4, 9, 16, 21, 22}, Table[(3 + (-1)^n + 2 n (n + 2))/4, {n, 6, 20}]] (* Eric W. Weisstein, Apr 18 2019 *)
Join[{1, 4, 9, 16, 21, 22}, LinearRecurrence[{2, 0, -2, 1}, {25, 32, 41, 50}, 20]] (* Eric W. Weisstein, Apr 18 2019 *)
CoefficientList[Series[(-1 - 2 x - x^2 + 4 x^4 + 6 x^5 - 4 x^6 - 8 x^7 + 4 x^9)/((-1 + x)^3 (1 + x)), {x, 0, 20}], x] (* Eric W. Weisstein, Apr 18 2019 *)
PROG
(PARI) Vec(x*(1 + 2*x + x^2 - 4*x^4 - 6*x^5 + 4*x^6 + 8*x^7 - 4*x^9) / ((1 - x)^3*(1 + x)) + O(x^40)) \\ Colin Barker, Jul 26 2019
CROSSREFS
Sequence in context: A313336 A313337 A127702 * A313338 A313339 A313340
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, Mar 26 2018
EXTENSIONS
Extended by Eric W. Weisstein, Apr 18 2019
Extended by Colin Barker, Jul 26 2019
STATUS
approved