A098647 Trace sequence associated to the 4 X 4 Krawtchouk matrix and its transpose.

1, 12, 224, 4608, 96256, 2015232, 42205184, 883949568, 18513657856, 387755016192, 8121246285824, 170093589823488, 3562486393470976, 74613683694600192, 1562729279488262144, 32730226951263879168

Offset: 0

Author

Paul Barry, Sep 18 2004

Keywords

• easy
• nonn

Comments

Let A=[1,1,1,1;3,1,-1,-3;3,-1,-1,3;1,-1,1,-1], the 4 X 4 Krawtchouk matrix. Then a(n)=trace((A*A')^n)/4.

Twelfth binomial transform of ((4*sqrt(5))^n +(-4*sqrt(5))^n)/2, with g.f. 1/(1-80*x^2).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..300
• Index entries for linear recurrences with constant coefficients, signature (24,-64).

Crossrefs

Cf. A098646.

Formula

G.f.: (1-12*x)/(1-24*x+64*x^2).

a(n) = ((12+4*sqrt(5))^n+(12-4*sqrt(5))^n)/2.

a(n) = 2^(n-1)*((sqrt(5)-1)^(2*n)+(sqrt(5)+1)^(2*n)).

a(n) = 4^n*A098648(n). - R. J. Mathar, Nov 11 2013