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 A128504 Row sums of array A128503 (second convolution of Chebyshev's S(n,x)=U(n,x/2) polynomials). 4

%I

%S 1,3,3,-2,-9,-9,3,18,18,-4,-30,-30,5,45,45,-6,-63,-63,7,84,84,-8,-108,

%T -108,9,135,135,-10,-165,-165,11,198,198,-12,-234,-234,13,273,273,-14,

%U -315,-315,15,360,360,-16,-408,-408,17,459,459

%N Row sums of array A128503 (second convolution of Chebyshev's S(n,x)=U(n,x/2) polynomials).

%C Second convolution of A010892.

%C Convolution of A099254 with A010892.

%C a(n) equals the coefficient of x^2 of the characteristic polynomial of the (n+2)X(n+2) tridiagonal matrix with 1's along the main diagonal, the superdiagonal, and the subdiagonal (see Mathematica code below). [_John M. Campbell_, Jul 10 2011]

%F a(n)=sum( A128503(n,m),m=0..floor(n/2)), n>=0.

%F G.f.: 1/(1-x+x^2)^3.

%F a(n) = (floor(n/3)+1)*(floor(n/3)-floor((n-1)/3)+(3/2)*(floor(n/3)+2)*(3*floor((n+1)/3)-n))*(-1)^n. - _Tani Akinari_, Jul 03 2013

%t Table[Coefficient[CharacteristicPolynomial[Array[KroneckerDelta[#1, #2] + KroneckerDelta[#1, #2 - 1] + KroneckerDelta[#1, #2 + 1] &, {n + 2, n + 2}], x], x^2], {n, 0, 70}] (* _John M. Campbell_, Jul 10 2011 *)

%o (PARI) Vec(1/(1-x+x^2)^3+O(x^66)) \\ _Joerg Arndt_, Jul 02 2013

%K sign,easy

%O 0,2

%A _Wolfdieter Lang_ Apr 04 2007

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Last modified June 19 09:33 EDT 2021. Contains 345126 sequences. (Running on oeis4.)