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%I #31 Sep 08 2022 08:46:00
%S 1,2,3,5,7,9,13,17,21,29,37,45,61,77,93,125,157,189,253,317,381,509,
%T 637,765,1021,1277,1533,2045,2557,3069,4093,5117,6141,8189,10237,
%U 12285,16381,20477,24573,32765,40957,49149,65533,81917,98301,131069,163837,196605
%N Partial sums of A173862.
%C Partial sums of powers of 2 repeated 3 times.
%H Vincenzo Librandi, <a href="/A200672/b200672.txt">Table of n, a(n) for n = 1..1000</a>
%H Shatalov A. A, <a href="http://www.world-science.ru/euro/119-20216">The Cupola Algorithm Data And The Modulation-37 The Natural Sciences Aspect And The Using For Analysis Of Ancient Layouts</a>, European Journal Of Natural History, 2007 No. 1, p. 35.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,2,-2).
%F G.f.: x*(1+x+x^2) / ( (x-1)*(2*x^3-1) ). - _R. J. Mathar_, Nov 28 2011
%F a(3*n) = 3*(2^n-1) = 3*A000225(n). - _Philippe Deléham_, Mar 13 2013
%F a(n) = 2*a(n-3) + 3 for n > 3. - _Yuchun Ji_, Nov 16 2018
%e a(4) = 1+1+1+2 = 5.
%t CoefficientList[Series[(1 + x + x^2) / ((x - 1) (2 x^3 - 1)), {x, 0, 50}], x] (* _Vincenzo Librandi_, Nov 16 2018 *)
%t Accumulate[Flatten[Table[PadRight[{},3,2^n],{n,0,20}]]] (* or *) LinearRecurrence[ {1,0,2,-2},{1,2,3,5},60] (* _Harvey P. Dale_, Jul 12 2022 *)
%o (BASIC) for i=0 to 12 : for j=1 to 3 : s=s+2^i : print s : next j : next i
%o (Magma) I:=[1,2,3,5]; [n le 4 select I[n] else Self(n-1) + 2*Self(n-3)- 2*Self(n-4): n in [1..50]]; // _Vincenzo Librandi_, Nov 16 2018
%Y Cf. A027383, A173862.
%K nonn
%O 1,2
%A _Jeremy Gardiner_, Nov 20 2011