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Search: id:A098647
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| A098647 |
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Trace sequence associated to the 4 X 4 Krawtchouk matrix and its transpose. |
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+0
3
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| 1, 12, 224, 4608, 96256, 2015232, 42205184, 883949568, 18513657856, 387755016192, 8121246285824, 170093589823488, 3562486393470976, 74613683694600192, 1562729279488262144, 32730226951263879168
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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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 ((4sqrt(5))^n +(-4sqrt(5))^n)/2, with g.f. 1/(1-80x^2).
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FORMULA
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G.f.: (1-12x)/(1-24x+64x^2); a(n)=((12+4sqrt(5))^n+(12-4sqrt(5))^n)/2; a(n)=2^(n-1)((sqrt(5)-1)^(2n)+(sqrt(5)+1)^(2n)).
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CROSSREFS
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Cf. A098646.
Adjacent sequences: A098644 A098645 A098646 this_sequence A098648 A098649 A098650
Sequence in context: A082165 A009176 A087585 this_sequence A034832 A089370 A089343
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Sep 18 2004
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