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A081182
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5-th binomial transform of (0,1,0,2,0,4,0,8,0,16,....).
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4
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0, 1, 10, 77, 540, 3629, 23870, 155233, 1003320, 6462841, 41552050, 266875157, 1713054420, 10992415589, 70523904230, 452413483753, 2902085040240, 18615340276081, 119405446835290, 765901642003037, 4912691142818700
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n)=10a(n-1)-23a(n-2), a(0)=0, a(1)=1. G.f. x/(1-10x+23x^2). a(n)=((5+sqrt(2))^n-(5-sqrt(2))^n/(2*sqrt(2)). a(n)=Sum {k=0..n, C(n, 2k+1)2^k*5^(n-2k-1) }
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MATHEMATICA
| Join[{a=0, b=1}, Table[c=10*b-23*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 27 2011*)
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PROG
| (Other) sage: [lucas_number1(n, 10, 23) for n in xrange(0, 21)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 26 2009]
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CROSSREFS
| Binomial transform of A081181.
Cf. A081183.
Sequence in context: A000808 A159579 A081678 * A127536 A016201 A080618
Adjacent sequences: A081179 A081180 A081181 * A081183 A081184 A081185
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Mar 12 2003
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