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%I #21 Nov 24 2018 08:11:12
%S 3,4,7,8,11,12,15,16,19,20,23,24,27,28,31,32,35,36,39,40,43,44,47,48,
%T 51,52,55,56,59,60,63,64,67,68,71,72,75,76,79,80,83,84,87,88,91,92,95,
%U 96,99,100,103,104,107,108,111,112,115,116,119,120,123,124,127,128,131,132,135,136,139,140
%N Numbers a such that b and c exist with b <= a < c and a*(a+1) + b^2 = c^2.
%C Numbers a such that a*(a+1) = c2 - b2 with b <= a < c let a(1)=3 then a(2*n) = a(2*n-1) + 1 and a(2*n+1) = a(2*n) + 3. [_Pierre CAMI_, Jan 15 2009]
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F a(1)=4; thereafter a(2*n) = a(2*n-1) + 3, a(2*n+1) = a(2*n) + 1.
%F a(n) = 4*n - a(n-1) - 1 (with a(1)=3). [_Vincenzo Librandi_, Nov 26 2010]
%F From _Colin Barker_, Mar 06 2013: (Start)
%F a(n) = (1 - (-1)^n + 4*n)/2.
%F a(n) = a(n-1) + a(n-2) - a(n-3).
%F G.f.: x*(x+3) / ((x-1)^2*(x+1)). (End)
%e 4*5 + 4*4 = 6*6; 7*8 + 5*5 = 9*9; 8*9 + 7*7 = 11*11;
%e 3*4 = 4*4 - 2*2; a(1)=3; 4*5 = 6*6 - 4*4; a(2) = 4; 7*6 = 9*9 - 5*5; a(3)=7. [_Pierre CAMI_, Jan 15 2009]
%t LinearRecurrence[{1,1,-1},{3,4,7},70] (* _Harvey P. Dale_, Jan 07 2016 *)
%Y Essentially the same as A014601. [_R. J. Mathar_, Nov 01 2009]
%K nonn,easy
%O 1,1
%A _Pierre CAMI_, Jan 14 2009, Jan 15 2009
%E More terms from _Vincenzo Librandi_, Nov 26 2010
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