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%I #29 Jun 29 2023 12:37:43
%S 3,1,3,9,27,81,243,729,2187,6561,19683,59049,177147,531441,1594323,
%T 4782969,14348907,43046721,129140163,387420489,1162261467,3486784401,
%U 10460353203,31381059609,94143178827,282429536481,847288609443,2541865828329
%N Binomial transform of A154879.
%C Binomial transform of the third differences of A001045.
%C The binomial transform of the first differences of A001045 is in A133494.
%C The binomial transform of the 2nd differences of A001045 is in A133494, with the sign of A133494(0) flipped.
%C The binomial transform of the p-th differences of A001045 is the number A077925(p-1) followed by A000244.
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (3).
%F From _Colin Barker_, Apr 05 2012: (Start)
%F a(n) = 3*a(n-1) for n > 1.
%F G.f.: (3-8*x)/(1-3*x). (End)
%F 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
%p read("transforms") ; A001045 := proc(n) option remember ; if n <= 1 then n; else procname(n-1)+2*procname(n-2) ; fi; end:
%p a001045 := [seq(A001045(n),n=0..80) ] ; a154879 := DIFF(DIFF(DIFF(a001045))) ; BINOMIAL(a154879) ; # _R. J. Mathar_, Jul 23 2009
%Y Cf. A154879, A078008. Essentially the same as A140429 and A000244.
%K nonn,easy,less
%O 0,1
%A _Paul Curtz_, Jan 26 2009
%E Edited and extended by _R. J. Mathar_, Jul 23 2009
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