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A098655 Trace sequence of 3 X 3 symmetric Krawtchouk matrix. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A206582 A154262 A154261 * A065038 A123225 A009028

Adjacent sequences:  A098652 A098653 A098654 * A098656 A098657 A098658

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 19 2004

STATUS

approved

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Last modified May 11 13:21 EDT 2021. Contains 343791 sequences. (Running on oeis4.)