A098655 - OEIS

%I #18 Sep 08 2019 12:09:06

%S 3,2,20,8,144,32,1088,128,8448,512,66560,2048,528384,8192,4210688,

%T 32768,33619968,131072,268697600,524288,2148532224,2097152,

%U 17184063488,8388608,137455730688,33554432,1099578736640,134217728,8796361457664

%N Trace sequence of 3 X 3 symmetric Krawtchouk matrix.

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

%H P. Feinsilver and J. Kocik, <a href="http://dx.doi.org/10.1007/0-387-23394-6_5">Krawtchouk Polynomials and Krawtchouk Matrices</a>, Contemporary Mathematics, 287 2001, pp. 83-96.

%H Philip Feinsilver, Jerzy Kocik, <a href="https://arxiv.org/abs/quant-ph/0702173">Krawtchouk matrices from classical and quantum random walks</a>, arXiv:quant-ph/0702173, 2007.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,8,-16).

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

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

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

%F E.g.f.: exp(2*x) + 2*cosh(2*sqrt(2)*x). - _Stefano Spezia_, Sep 08 2019

%Y Cf. A098656, A098657.

%K easy,nonn

%O 0,1

%A _Paul Barry_, Sep 19 2004