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A155734
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Binomial transform of A154879.
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0
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3, 1, 3, 9, 27, 81, 243, 729, 2187, 6561, 19683, 59049, 177147, 531441, 1594323, 4782969, 14348907, 43046721, 129140163, 387420489, 1162261467, 3486784401, 10460353203, 31381059609, 94143178827, 282429536481, 847288609443, 2541865828329
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OFFSET
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0,1
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COMMENTS
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Binomial transform of the third differences of A001045.
The binomial transform of the first differences of A001045 is in A133494.
The binomial transform of the 2nd differences of A001045 is in A133494, with the sign of A133494(0) flipped.
The binomial transform of the p-th differences of A001045 is the number A077925(p-1) followed by A000244.
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LINKS
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FORMULA
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a(n) = 3*a(n-1) for n > 1.
G.f.: (3-8*x)/(1-3*x). (End)
G.f.: (1 - 2/G(0))/x where G(k) = 1 + 2^k/(1 - 2*x/(2*x + 2^k/G(k+1))); (recursively defined continued fraction). - Sergei N. Gladkovskii, Dec 06 2012
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MAPLE
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read("transforms") ; A001045 := proc(n) option remember ; if n <= 1 then n; else procname(n-1)+2*procname(n-2) ; fi; end:
a001045 := [seq(A001045(n), n=0..80) ] ; a154879 := DIFF(DIFF(DIFF(a001045))) ; BINOMIAL(a154879) ; # R. J. Mathar, Jul 23 2009
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CROSSREFS
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KEYWORD
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nonn,easy,less
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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