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A081179
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3rd binomial transform of (0,1,0,2,0,4,0,8,0,16,....).
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7
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0, 1, 6, 29, 132, 589, 2610, 11537, 50952, 224953, 993054, 4383653, 19350540, 85417669, 377052234, 1664389721, 7346972688, 32431108081, 143157839670, 631929281453, 2789470811028, 12313319895997, 54353623698786
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Binomial transform of 0, 1, 4, 14, 48,... (A007070 with offset 1) and second binomial transform of A000129. - R. J. Mathar, Dec 10 2011
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (6,-7).
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FORMULA
| a(n)=6a(n-1)-7a(n-2), a(0)=0, a(1)=1. G.f.: x/(1-6x+7x^2). a(n)=((3+sqrt(2))^n-(3-sqrt(2))^n)/(2*sqrt(2)). [Corrected by Al Hakanson (hawkuu(AT)gmail.com), Dec 27 2008]
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MATHEMATICA
| Join[{a=0, b=1}, Table[c=6*b-7*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 18 2011*)
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PROG
| (Other) sage: [lucas_number1(n, 6, 7) for n in xrange(0, 23)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
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CROSSREFS
| Cf. A081180.
Sequence in context: A008549 A026675 A026873 * A026866 A045445 A026884
Adjacent sequences: A081176 A081177 A081178 * A081180 A081181 A081182
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 11 2003
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