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A060188 A column and diagonal of A060187.

%I A060188 #50 Sep 03 2024 09:35:19
%S A060188 1,6,23,76,237,722,2179,6552,19673,59038,177135,531428,1594309,
%T A060188 4782954,14348891,43046704,129140145,387420470,1162261447,3486784380,
%U A060188 10460353181,31381059586,94143178803,282429536456,847288609417
%N A060188 A column and  diagonal of A060187.
%C A060188 Sums of rows of the numerators and of the denominators of the redundant Stern-Brocot structure A152975/A152976: a(n+2) = Sum_{k=2^n..(2^(n+1) -1)} A152975(k) = Sum_{k=2^n..(2^(n+1) -1)} A152976(k). - _Reinhard Zumkeller_, Dec 22 2008
%H A060188 Vincenzo Librandi, <a href="/A060188/b060188.txt">Table of n, a(n) for n = 2..2000</a>
%H A060188 P. A. MacMahon, <a href="https://doi.org/10.1112/plms/s2-19.1.305">The divisors of numbers</a>, Proc. London Math. Soc., (2) 19 (1920), 305-340; Coll. Papers II, pp. 267-302.
%H A060188 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,-7,3).
%F A060188 a(n) = 3^(n-1) - n = A061980(n-1, 2). - _Henry Bottomley_, May 24 2001
%F A060188 From _Paul Barry_, Jun 24 2003: (Start)
%F A060188 With offset 0, this is 3^(n+1) - n - 2.
%F A060188 Partial sums of A048473. (End)
%F A060188 From _Colin Barker_, Dec 19 2012: (Start)
%F A060188 a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3).
%F A060188 G.f.: x^2*(1 + x)/((1-x)^2*(1-3*x)). (End)
%F A060188 E.g.f.: (exp(3*x) - 3*x*exp(x) - 1)/3. - _Wolfdieter Lang_, Apr 17 2017
%p A060188 a[0]:=1:for n from 1 to 24 do a[n]:=(4*a[n-1]-3*a[n-2]+2) od: seq(a[n], n=0..24); # _Zerinvary Lajos_, Jun 08 2007
%t A060188 Table[3^(n-1) -n, {n,2,30}] (* _Vladimir Joseph Stephan Orlovsky_, Nov 15 2008 *)
%t A060188 LinearRecurrence[{5,-7,3},{1,6,23},30] (* _Harvey P. Dale_, Jul 03 2024 *)
%o A060188 (Magma) [3^(n-1)-n: n in [2..30]]; // _Vincenzo Librandi_, Sep 05 2011
%o A060188 (Sage) [3^(n-1) -n for n in (2..32)] # _G. C. Greubel_, Jan 07 2022
%Y A060188 Cf. A048473, A060187 (first differences).
%K A060188 nonn,easy
%O A060188 2,2
%A A060188 _N. J. A. Sloane_, Mar 20 2001
%E A060188 More terms from _Vladeta Jovovic_, Mar 20 2001