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A098647 Trace sequence associated to the 4 X 4 Krawtchouk matrix and its transpose. 4
1, 12, 224, 4608, 96256, 2015232, 42205184, 883949568, 18513657856, 387755016192, 8121246285824, 170093589823488, 3562486393470976, 74613683694600192, 1562729279488262144, 32730226951263879168 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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).

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

CROSSREFS

Cf. A098646.

Sequence in context: A214512 A220068 A247745 * A300561 A290754 A318417

Adjacent sequences:  A098644 A098645 A098646 * A098648 A098649 A098650

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Sep 18 2004

STATUS

approved

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Last modified March 31 18:53 EDT 2020. Contains 333151 sequences. (Running on oeis4.)