A098655 Trace sequence of 3 X 3 symmetric Krawtchouk matrix.

3, 2, 20, 8, 144, 32, 1088, 128, 8448, 512, 66560, 2048, 528384, 8192, 4210688, 32768, 33619968, 131072, 268697600, 524288, 2148532224, 2097152, 17184063488, 8388608, 137455730688, 33554432, 1099578736640, 134217728, 8796361457664

Offset

0,1

Comments

Let A=[1,2,1;2,0,-2;1,-2,1] the 3 X 3 symmetric Krawtchouk matrix. Then a(n) = trace(A^n).

Links

Table of n, a(n) for n=0..28.

P. Feinsilver and J. Kocik, Krawtchouk Polynomials and Krawtchouk Matrices, Contemporary Mathematics, 287 2001, pp. 83-96.

Philip Feinsilver, Jerzy Kocik, Krawtchouk matrices from classical and quantum random walks, arXiv:quant-ph/0702173, 2007.

Index entries for linear recurrences with constant coefficients, signature (2,8,-16).

Formula

G.f.: (3 - 4*x - 8*x^2)/((1-2*x)*(1-8*x^2)).

a(n) = 2^n + (2*sqrt(2))^n + (-2*sqrt(2))^n.

a(n) = 2*a(n-1) + 8*a(n-2) - 16*a(n-3).

E.g.f.: exp(2*x) + 2*cosh(2*sqrt(2)*x). - Stefano Spezia, Sep 08 2019

Crossrefs

Cf. A098656, A098657.

Sequence in context: A154262 A367548 A154261 * A065038 A123225 A009028

Adjacent sequences: A098652 A098653 A098654 * A098656 A098657 A098658

Keyword

easy,nonn

Author

Paul Barry, Sep 19 2004

Status

approved