A140883 - OEIS

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A140883

Triangle T(n,k) = A053120(n,k)+A053120(n,n-k) of symmetrized Chebyshev coefficients, read by rows, 0<=k<=n.

2, 1, 1, 1, 0, 1, 4, -3, -3, 4, 9, 0, -16, 0, 9, 16, 5, -20, -20, 5, 16, 31, 0, -30, 0, -30, 0, 31, 64, -7, -112, 56, 56, -112, -7, 64, 129, 0, -288, 0, 320, 0, -288, 0, 129, 256, 9, -576, -120, 432, 432, -120, -576, 9, 256, 511, 0, -1230, 0, 720, 0, 720, 0, -1230, 0, 511

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

Row sums are constantly two.

LINKS

Table of n, a(n) for n=0..65.

FORMULA

T(n,k) = T(n,n-k).

EXAMPLE

1, 1;

1, 0, 1;

4, -3, -3, 4;

9, 0, -16, 0, 9;

16, 5, -20, -20, 5, 16;

31, 0, -30, 0, -30, 0, 31;

64, -7, -112, 56, 56, -112, -7, 64;

129, 0, -288, 0, 320, 0, -288, 0, 129;

256, 9, -576, -120, 432, 432, -120, -576, 9, 256;

511, 0, -1230, 0, 720, 0, 720, 0, -1230, 0, 511;

MATHEMATICA

Clear[p, x, n, m, a]; p[x_, n_] := ChebyshevT[n, x] + ExpandAll[x^n*ChebyshevT[n, 1/x]]; Table[p[x, n], {n, 0, 10}]; a = Table[CoefficientList[p[x, n], x], {n, 0, 10}]; Flatten[a]

CROSSREFS

Cf. A053120.

Sequence in context: A348652 A117274 A221650 * A214021 A260516 A064744

Adjacent sequences: A140880 A140881 A140882 * A140884 A140885 A140886

KEYWORD

tabl,sign

AUTHOR

Roger L. Bagula and Gary W. Adamson, Jul 22 2008

STATUS

approved