This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A155734 #29 Jun 29 2023 12:37:43
%S A155734 3,1,3,9,27,81,243,729,2187,6561,19683,59049,177147,531441,1594323,
%T A155734 4782969,14348907,43046721,129140163,387420489,1162261467,3486784401,
%U A155734 10460353203,31381059609,94143178827,282429536481,847288609443,2541865828329
%N A155734 Binomial transform of A154879.
%C A155734 Binomial transform of the third differences of A001045.
%C A155734 The binomial transform of the first differences of A001045 is in A133494.
%C A155734 The binomial transform of the 2nd differences of A001045 is in A133494, with the sign of A133494(0) flipped.
%C A155734 The binomial transform of the p-th differences of A001045 is the number A077925(p-1) followed by A000244.
%H A155734 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (3).
%F A155734 From _Colin Barker_, Apr 05 2012: (Start)
%F A155734 a(n) = 3*a(n-1) for n > 1.
%F A155734 G.f.: (3-8*x)/(1-3*x). (End)
%F A155734 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 A155734 read("transforms") ; A001045 := proc(n) option remember ; if n <= 1 then n; else procname(n-1)+2*procname(n-2) ; fi; end:
%p A155734 a001045 := [seq(A001045(n),n=0..80) ] ; a154879 := DIFF(DIFF(DIFF(a001045))) ; BINOMIAL(a154879) ; # _R. J. Mathar_, Jul 23 2009
%Y A155734 Cf. A154879, A078008. Essentially the same as A140429 and A000244.
%K A155734 nonn,easy,less
%O A155734 0,1
%A A155734 _Paul Curtz_, Jan 26 2009
%E A155734 Edited and extended by _R. J. Mathar_, Jul 23 2009