%I #8 Nov 06 2018 12:46:28
%S 1,2,7,10,13,18,20,25,27,32,34,37,40,45,49,51,54,57,62,66,68,71,74,79,
%T 83,85,90,92,97,99,102,105,110,112,115,120,124,126,131,133,138,140,
%U 143,146,151,153,156,161,165,167,172,174,179,181,184,187,192,194
%N Solution of the complementary equation a(n) = a(1)*b(n1)  a(0)*b(n2) + 2*n  2, where a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, and (b(n)) is the increasing sequence of positive integers not in (a(n)). See Comments.
%C The increasing complementary sequences a() and b() are uniquely determined by the titular equation and initial values. See A297830 for a guide to related sequences.
%C a(n)  (2+sqrt(2))*n < 2 for n >= 1.
%H Clark Kimberling, <a href="/A297832/b297832.txt">Table of n, a(n) for n = 0..10000</a>
%e a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, so that a(2) = 7.
%e Complement: (b(n)) = (3,4,5,7,8,10,12,13,15,17,18,19,...)
%t a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4;
%t a[n_] := a[n] = a[1]*b[n  1]  a[0]*b[n  2] + 2 n  2;
%t j = 1; While[j < 100, k = a[j]  j  1;
%t While[k < a[j + 1]  j + 1, b[k] = j + k + 2; k++]; j++]; k
%t Table[a[n], {n, 0, k}] (* A297832 *)
%Y Cf. A297826, A297830.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, Feb 04 2018
