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Search: id:A098648
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| A098648 |
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Expansion of (1-3x)/(1-6x+4x^2). |
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+0
2
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| 1, 3, 14, 72, 376, 1968, 10304, 53952, 282496, 1479168, 7745024, 40553472, 212340736, 1111830528, 5821620224, 30482399232, 159607914496, 835717890048, 4375875682304, 22912382533632, 119970792472576, 628175224700928
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Binomial transform of A001077. Second binomial transform of A084057. Third binomial transform of 1/(1-5x^2). 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((16(A*A`)^(-1))^n)/4.
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LINKS
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Zerinvary Lajos, Sage Notebooks
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FORMULA
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E.g.f.: exp(3x)cosh(sqrt(5)x); a(n)=((3-sqrt(5))^n+(3+sqrt(5))^n)/2.
a(n)=2*(3*a(n-1)-2*a(n-2)). - Lekraj Beedassy (blekraj(AT)yahoo.com), Oct 22 2004
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PROGRAM
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sage: [lucas_number2(n, 6, 4)/2 for n in xrange(0, 25)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2008
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CROSSREFS
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Cf. A098647.
Sequence in context: A009020 A109792 A009637 this_sequence A026295 A118650 A080238
Adjacent sequences: A098645 A098646 A098647 this_sequence A098649 A098650 A098651
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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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