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A173335 A triangle of coefficients based on the squares of the Chebyshev T and U polynomials: p(x,n)=If[Mod[n, 2] == 0, (ChebyshevT[n + 1, x]^2 + x^2*ChebyshevU[n, x]^2)/(2*x^2), (-1 + ChebyshevT[n + 1, x]^2 + x^2*ChebyshevU[n, x]^2)/(2*x^2)] 0
1, -2, 0, 4, 5, 0, -16, 0, 16, -8, 0, 48, 0, -96, 0, 64, 13, 0, -112, 0, 368, 0, -512, 0, 256, -18, 0, 228, 0, -1088, 0, 2432, 0, -2560, 0, 1024, 25, 0, -416, 0, 2720, 0, -8704, 0, 14592, 0, -12288, 0, 4096, -32, 0, 704, 0, -6016, 0, 25856, 0, -61440, 0, 81920, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums are:A000982;

{1, 2, 5, 8, 13, 18, 25, 32, 41, 50, 61,...}.

LINKS

Table of n, a(n) for n=0..60.

FORMULA

p(x,n)=If[Mod[n, 2] == 0, (ChebyshevT[n + 1, x]^2 + x^2*ChebyshevU[n, x]^2)/(2*x^2),

(-1 + ChebyshevT[n + 1, x]^2 + x^2*ChebyshevU[n, x]^2)/(2*x^2)]

EXAMPLE

{1},

{-2, 0, 4},

{5, 0, -16, 0, 16},

{-8, 0, 48, 0, -96, 0, 64},

{13, 0, -112, 0, 368, 0, -512, 0, 256},

{-18, 0, 228, 0, -1088, 0, 2432, 0, -2560, 0, 1024},

{25, 0, -416, 0, 2720, 0, -8704, 0, 14592, 0, -12288, 0, 4096},

{-32, 0, 704, 0, -6016, 0, 25856, 0, -61440, 0, 81920, 0, -57344, 0, 16384},

{41, 0, -1120, 0, 12128, 0, -67072, 0, 211712, 0, -397312, 0, 438272, 0, -262144, 0, 65536},

{-50, 0, 1700, 0, -22720, 0, 156800, 0, -630272, 0, 1559552, 0, -2408448, 0, 2260992, 0, -1179648, 0, 262144},

{61, 0, -2480, 0, 40112, 0, -337408, 0, 1676032, 0, -5242880, 0, 10616832, 0, -13893632, 0, 11337728, 0, -5242880, 0, 1048576}

MATHEMATICA

p[x_, n_] = If[Mod[n, 2] == 0, (ChebyshevT[n + 1, x]^2 + x^2* ChebyshevU[n, x]^2)/(2*x^2),

(-1 + ChebyshevT[n + 1, x]^2 + x^2*ChebyshevU[n, x]^2)/(2*x^2)];

Table[CoefficientList[p[x, n], x], {n, 0, 10}];

Flatten[%]

CROSSREFS

A000982

Sequence in context: A100050 A164616 A258100 * A201837 A004482 A111677

Adjacent sequences:  A173332 A173333 A173334 * A173336 A173337 A173338

KEYWORD

sign,tabf,uned

AUTHOR

Roger L. Bagula, Feb 16 2010

STATUS

approved

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Last modified November 16 02:33 EST 2018. Contains 317252 sequences. (Running on oeis4.)