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 A284966 Triangle read by rows: coefficients of the scaled Lucas polynomials x^(n/2) L(n, sqrt(x)). 1
 0, 1, 0, 2, 1, 0, 0, 3, 1, 0, 0, 2, 4, 1, 0, 0, 0, 5, 5, 1, 0, 0, 0, 2, 9, 6, 1, 0, 0, 0, 0, 7, 14, 7, 1, 0, 0, 0, 0, 2, 16, 20, 8, 1, 0, 0, 0, 0, 0, 9, 30, 27, 9, 1, 0, 0, 0, 0, 0, 2, 25, 50, 35, 10, 1, 0, 0, 0, 0, 0, 0, 11, 55, 77, 44, 11, 1, 0, 0, 0, 0, 0, 0, 2, 36, 105, 112, 54, 12, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS For n >= 3, also the coefficients of the edge and vertex cover polynomials for the n-cycle graph C_n. LINKS Eric Weisstein's World of Mathematics, Cycle Graph Eric Weisstein's World of Mathematics, Edge Cover Polynomial Eric Weisstein's World of Mathematics, Lucas Polynomia Eric Weisstein's World of Mathematics, Vertex Cover Polynomial EXAMPLE First few polynomials are 2 x 2 x + x^2 3 x^2 + x 2 x^2 + 4 x^3 + x^4 giving 2; 0, 1; 0, 2, 1; 0, 0, 3, 1; 0, 0, 2, 4, 1; 0, 0, 0, 5, 5, 1; ... MATHEMATICA CoefficientList[Table[x^(n/2) LucasL[n, Sqrt[x]], {n, 12}], x] // Flatten (* Eric W. Weisstein, Apr 06 2017 *) CoefficientList[Table[2 x^n (-1/x)^(n/2) ChebyshevT[n, 1/(2 Sqrt[-1/x])], {n, 12}], x] // Flatten (* Eric W. Weisstein, Apr 06 2017 *) CoefficientList[Table[FunctionExpand[2 (-(1/x))^(n/2) x^n Cos[n ArcSec[2 Sqrt[-(1/x)]]]], {n, 15}], x] // Flatten (* Eric W. Weisstein, Apr 06 2017 *) CoefficientList[LinearRecurrence[{x, x}, {x, x (2 + x)}, 15], x] // Flatten (* Eric W. Weisstein, Apr 06 2017 *) CROSSREFS Cf. A034807 (Lucas polynomials x^(n/2) L(n, 1/sqrt(x)). Cf. A111125, A127677, A136481. Sequence in context: A105820 A136263 A105593 * A029371 A114374 A111505 Adjacent sequences:  A284963 A284964 A284965 * A284967 A284968 A284969 KEYWORD nonn,easy,tabl AUTHOR Eric W. Weisstein, Apr 06 2017 STATUS approved

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Last modified October 24 01:20 EDT 2018. Contains 316541 sequences. (Running on oeis4.)