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A364587 revision #14

A364587
Clique covering number, independence number, and Shannon capacity of the n-Lucas cube graph.
0
1, 2, 3, 4, 6, 10, 15, 24, 39, 62, 100, 162, 261, 422, 683, 1104, 1786, 2890, 4675, 7564, 12239, 19802, 32040, 51842, 83881, 135722, 219603, 355324, 574926, 930250, 1505175, 2435424, 3940599, 6376022, 10316620, 16692642, 27009261, 43701902, 70711163, 114413064
OFFSET
1,2
LINKS
E. Munarini, C. Perelli Cippo, and N. Zagaglia Salvi. On the Lucas Cubes. Fibonacci Quart. 39 (2001), 12-21.
Eric Weisstein's World of Mathematics, Clique Covering Number
Eric Weisstein's World of Mathematics, Independence Number
Eric Weisstein's World of Mathematics, Lucas Cube Graph
Eric Weisstein's World of Mathematics, Shanon Capacity
FORMULA
a(n) = (4 + 3*LucasL[n] + 2*cos(2*n*Pi/3))/6.
a(n) = a(n-1) + a(n-2) + a(n-3) - a(n-4) - a(n-5).
G.f.: x*(1+x-2*x^3-2*x^4)/(1-x-x^2-x^3+x^4+x^5).
MATHEMATICA
Table[(4 + 3 LucasL[n] + 2 Cos[2 n Pi/3])/6, {n, 20}]
LinearRecurrence[{1, 1, 1, -1, -1}, {1, 2, 3, 4, 6}, 20]
CoefficientList[Series[(1 + x - 2 x^3 - 2 x^4)/(1 - x - x^2 - x^3 + x^4 + x^5), {x, 0, 20}], x]
CROSSREFS
Sequence in context: A018062 A222121 A221995 * A221996 A070542 A098855
KEYWORD
nonn
AUTHOR
Eric W. Weisstein, Jul 29 2023
STATUS
editing