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Search: id:A081180
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| A081180 |
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4-th binomial transform of (0,1,0,2,0,4,0,8,0,16,....). |
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+0
6
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| 0, 1, 8, 50, 288, 1604, 8800, 47944, 260352, 1411600, 7647872, 41420576, 224294400, 1214467136, 6575615488, 35602384000, 192760455168, 1043650265344, 5650555750400, 30593342288384, 165638957801472, 896804870374400
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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a(n)=8a(n-1)-14a(n-2), a(0)=0, a(1)=1. G.f.: x/(1-8x+14x^2). a(n)=((4+sqrt(2))^n-(4-sqrt(2))^n/(2*sqrt(2)). a(n)=Sum {k=0..n, C(n, 2k+1)2^k*4^(n-2k-1) }
If shifted once left, fourth binomial transform of A143095 [From Al Hakanson (hawkuu(AT)gmail.com), Jul 25 2009, R. J. Mathar Oct 15 2009]
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PROGRAM
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(Other) sage: [lucas_number1(n, 8, 14) for n in xrange(0, 22)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 23 2009]
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CROSSREFS
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Binomial transform of A081179.
Cf. A081182.
Sequence in context: A030279 A133357 A081675 this_sequence A052177 A115598 A127745
Adjacent sequences: A081177 A081178 A081179 this_sequence A081181 A081182 A081183
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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), Mar 11 2003
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EXTENSIONS
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Modified the competing comment on the fourth binomial transform - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 15 2009
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