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A081184
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7-th binomial transform of (0,1,0,2,0,4,0,8,0,16,....).
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3
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0, 1, 14, 149, 1428, 12989, 114730, 995737, 8548008, 72872473, 618458246, 5233409213, 44200191420, 372832446869, 3142245259426, 26468308629121, 222870793614672, 1876180605036721, 15791601170624510, 132901927952017253
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| a(n)=14a(n-1)-47a(n-2), a(0)=0, a(1)=1. G.f. x/(1-14x+47x^3). a(n)=((7+sqrt(2))^n-(7-sqrt(2))^n/(2*sqrt(2)). a(n)=Sum {k=0..n, C(n, 2k+1)2^k*7^(n-2k-1) }.
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MATHEMATICA
| Join[{a=1, b=14}, Table[c=14*b-47*a; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Feb 01 2011*)
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CROSSREFS
| Binomial transform of A081183.
Cf. A081185, A081183.
Sequence in context: A065899 A162965 A067103 * A032343 A019521 A009614
Adjacent sequences: A081181 A081182 A081183 * A081185 A081186 A081187
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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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