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A128495 Coefficient table for sums of squares of Chebyshev's S-Polynomials. 5


%S 1,1,1,2,-1,1,2,3,-3,1,3,-3,8,-5,1,3,6,-16,17,-7,1,4,-6,30,-45,30,-9,

%T 1,4,10,-50,103,-98,47,-11,1,5,-10,80,-211,269,-183,68,-13,1,5,15,

%U -120,399,-651,588,-308,93,-15,1,6,-15,175,-707,1432,-1644,1136,-481,122,-17,1,6,21,-245,1190,-2920,4132,-3608

%N Coefficient table for sums of squares of Chebyshev's S-Polynomials.

%C See A049310 for the coefficient table of Chebyshev's S(n,x)=U(n,x/2) polynomials.

%C The triangle for the coefficients of x^2 in S(n,x)^2 is A158454. - _Wolfdieter Lang_, Oct 18 2012

%H W. Lang, <a href="/A128495/a128495.txt">First 15 rows.</a>

%F S(2;n,x):=sum(S(k,x)^2,k=0..n)=sum(a(n,m)*x^(2*m),m=0..n), n>=0.

%F a(n,m)=[x^m](n+2-T(n+1,x/2)*U(n+1,x/2))/(2*(1-(x/2)^2)).

%e [1]; [1,1]; [2,-1,1]; [2,3,-3,1]; [3,-3,8,-5,1]; [3,6,-16,17,-7,1]; ...

%e Row polynomial S(2;4,x)=3-3*x^2+8*x^4-5*x^6+x^8 = sum(S(k,x)^2,k=0..4).

%e (4+2-T(4+1,x/2)*U(4+1,x/2))/(2*(1-(x/2)^2))= S(2;4,x)

%Y Row sums (signed) look like: A004523. Row sums (unsigned): A128496.

%Y Cf. A128494 =S(1; n, m).

%K sign,easy,tabl

%O 0,4

%A _Wolfdieter Lang_ Apr 04 2007

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Last modified July 12 13:27 EDT 2020. Contains 335663 sequences. (Running on oeis4.)