# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a294480 Showing 1-1 of 1 %I A294480 #5 Nov 01 2017 12:27:23 %S A294480 1,3,9,14,23,31,43,55,70,85,103,122,143,165,189,214,241,269,299,331, %T A294480 364,399,435,473,512,553,596,640,686,733,782,832,884,937,992,1048, %U A294480 1106,1166,1227,1290,1354,1420,1487,1556,1626,1698,1771,1846,1923,2001,2081 %N A294480 Solution of the complementary equation a(n) = a(n-2) + b(n-1) + 2n, where a(0) = 1, a(1) = 3, b(0) = 2. %C A294480 The complementary sequences a() and b() are uniquely determined by the titular equation and initial values. See A294476 for a guide to related sequences. %H A294480 Clark Kimberling, Table of n, a(n) for n = 0..1000 %H A294480 Clark Kimberling, Complementary equations, J. Int. Seq. 19 (2007), 1-13. %e A294480 a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4, so that %e A294480 a(2) = a(0) + b(1) = 9 %e A294480 Complement: (b(n)) = (2, 4, 5, 6, 7, 8, 10, 12, 13, 15, ...) %t A294480 mex := First[Complement[Range[1, Max[#1] + 1], #1]] &; %t A294480 a[0] = 1; a[1] = 3; b[0] = 2; %t A294480 a[n_] := a[n] = a[n - 2] + b[n - 1] + 2n; %t A294480 b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]]; %t A294480 Table[a[n], {n, 0, 40}] (* A294480 *) %t A294480 Table[b[n], {n, 0, 10}] %Y A294480 Cf. A293076, A293765, A294476. %K A294480 nonn,easy %O A294480 0,2 %A A294480 _Clark Kimberling_, Nov 01 2017 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE