

A123583


Triangle read by rows: T(n, k) is the coefficient of x^k in the polynomial 1  T_n(x)^2, where T_n(x) is the nth Chebyshev polynomial of the first kind.


8



0, 1, 0, 1, 0, 0, 4, 0, 4, 1, 0, 9, 0, 24, 0, 16, 0, 0, 16, 0, 80, 0, 128, 0, 64, 1, 0, 25, 0, 200, 0, 560, 0, 640, 0, 256, 0, 0, 36, 0, 420, 0, 1792, 0, 3456, 0, 3072, 0, 1024, 1, 0, 49, 0, 784, 0, 4704, 0, 13440, 0, 19712, 0, 14336, 0, 4096, 0, 0, 64, 0, 1344, 0, 10752, 0, 42240, 0, 90112, 0, 106496, 0, 65536, 0
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OFFSET

0,7


COMMENTS

All row sum are zero. Row sums of absolute values are in A114619.  Klaus Brockhaus, May 29 2009


REFERENCES

Gareth Jones and David Singerman, Belyi Functions, Hypermaps and Galois Groups, Bull. London Math. Soc., 28 (1996), 561590.
G. B. Shabat and I. A. Voevodskii, Drawing curves over number fields, The Grothendieck Festschift, vol. 3, Birkhaeuser, 1990, 199227.
G. B. Shabat and A. Zvonkin, Plane trees and algebraic numbers, Contemporary Math., 1994, vol. 178, 233275.


LINKS

Table of n, a(n) for n=0..79.
Yuri Matiyasevich, Generalized Chebyshev polynomials.


EXAMPLE

First few rows of the triangle are:
[ 0 ]
[ 1, 0, 1 ]
[ 0, 0, 4, 0, 4 ]
[ 1, 0, 9, 0, 24, 0, 16 ]
[ 0, 0, 16, 0, 80, 0, 128, 0, 64 ]
[ 1, 0, 25, 0, 200, 0, 560, 0, 640, 0, 256 ]
[ 0, 0, 36, 0, 420, 0, 1792, 0, 3456, 0, 3072, 0, 1024 ]
First few polynomials are:
0,
1  x^2,
4 x^2  4 x^4,
1  9 x^2 + 24 x^4  16 x^6,
16 x^2  80 x^4 + 128 x^6  64 x^8,
1  25 x^2 + 200 x^4  560 x^6 + 640 x^8  256 x^10,
36 x^2  420 x^4 + 1792 x^6  3456 x^8 + 3072 x^10  1024 x^12.


MATHEMATICA

w = Table[CoefficientList[1  ChebyshevT[n, x]^2, x], {n, 0, 10}]; Flatten[w]


PROG

(MAGMA) [0] cat &cat[ Coefficients(1ChebyshevT(n)^2): n in [1..8] ];
(PARI) v=[]; for(n=0, 8, v=concat(v, vector(2*n+1, j, polcoeff(1poltchebi(n)^2, j1)))); v


CROSSREFS

Cf. A123588.
Sequence in context: A112919 A019201 A137660 * A236112 A226787 A140574
Adjacent sequences: A123580 A123581 A123582 * A123584 A123585 A123586


KEYWORD

tabf,sign


AUTHOR

Gary W. Adamson and Roger L. Bagula, Nov 12 2006


EXTENSIONS

Edited by N. J. A. Sloane, Mar 09 2008


STATUS

approved



