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A152891 a(1) = b(1) = 0; for n > 1, b(n) = b(n-1) + n-1 + a(n-1) and a(n) = a(n-1) + n-1 + b(n).

%I A152891 #31 Aug 04 2020 19:46:55
%S A152891 0,2,9,29,83,226,602,1588,4171,10935,28645,75012,196404,514214,
%T A152891 1346253,3524561,9227447,24157798,63245966,165580120,433494415,
%U A152891 1134903147,2971215049,7778742024,20365011048,53316291146,139583862417
%N A152891 a(1) = b(1) = 0; for n > 1, b(n) = b(n-1) + n-1 + a(n-1) and a(n) = a(n-1) + n-1 + b(n).
%C A152891 Partial sums of A035508. - _R. J. Mathar_, Dec 15 2008
%H A152891 Harvey P. Dale, <a href="/A152891/b152891.txt">Table of n, a(n) for n = 1..1000</a>
%H A152891 Guo-Niu Han, <a href="/A196265/a196265.pdf">Enumeration of Standard Puzzles</a>, 2011. [Cached copy]
%H A152891 Guo-Niu Han, <a href="https://arxiv.org/abs/2006.14070">Enumeration of Standard Puzzles</a>, arXiv:2006.14070 [math.CO], 2020.
%H A152891 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-8,5,-1).
%F A152891 From _R. J. Mathar_, Dec 15 2008: (Start)
%F A152891 G.f.: x^2*(2 - x)/((1 - 3*x + x^2)*(1 - x)^2).
%F A152891 a(n) = A001906(n+1) - A001906(n) - n - 1. (End)
%F A152891 a(n) = Fibonacci(2*n+1) - n - 1. - _Emeric Deutsch_, Jun 01 2009
%p A152891 with(combinat): seq(fibonacci(2*n+1)-n-1, n = 1 .. 27); # _Emeric Deutsch_, Jun 01 2009
%t A152891 lst={};a=b=0;Do[b+=n+a;a+=n+b;AppendTo[lst,a],{n,0,2*4!}];lst
%t A152891 Table[Fibonacci[2n+1]-n-1,{n,30}] (* or *) LinearRecurrence[{5,-8,5,-1},{0,2,9,29},30] (* _Harvey P. Dale_, Sep 24 2013 *)
%Y A152891 Cf. A000045, A001906, A035508, A054452 (b sequence).
%K A152891 nonn
%O A152891 1,2
%A A152891 _Vladimir Joseph Stephan Orlovsky_, Dec 14 2008
%E A152891 Name corrected by _Jon E. Schoenfield_, Feb 19 2019