

A128504


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


3



1, 3, 3, 2, 9, 9, 3, 18, 18, 4, 30, 30, 5, 45, 45, 6, 63, 63, 7, 84, 84, 8, 108, 108, 9, 135, 135, 10, 165, 165, 11, 198, 198, 12, 234, 234, 13, 273, 273, 14, 315, 315, 15, 360, 360, 16, 408, 408, 17, 459, 459
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OFFSET

0,2


COMMENTS

Second convolution of A010892.
Convolution of A099254 with A010892.
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]


LINKS

Table of n, a(n) for n=0..50.


FORMULA

a(n)=sum( A128503(n,m),m=0..floor(n/2)), n>=0.
G.f.: 1/(1x+x^2)^3.
a(n) = (floor(n/3)+1)*(floor(n/3)floor((n1)/3)+(3/2)*(floor(n/3)+2)*(3*floor((n+1)/3)n))*(1)^n.  Tani Akinari, Jul 03 2013


MATHEMATICA

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 *)


PROG

(PARI) Vec(1/(1x+x^2)^3+O(x^66)) \\ Joerg Arndt, Jul 02 2013


CROSSREFS

Sequence in context: A248569 A214101 A100052 * A193822 A202699 A058137
Adjacent sequences: A128501 A128502 A128503 * A128505 A128506 A128507


KEYWORD

sign,easy


AUTHOR

Wolfdieter Lang Apr 04 2007


STATUS

approved



