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 A294385 Solution of the complementary equation a(n) = a(n-1)*b(n-2) + n, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4. 2
 1, 3, 8, 35, 179, 1079, 7559, 68038, 680388, 7484277, 89811334, 1167547353, 16345662954 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The complementary sequences a() and b() are uniquely determined by the titular equation and initial values. See A294381) for a guide to related sequences. LINKS Clark Kimberling, Complementary equations, J. Int. Seq. 19 (2007), 1-13. EXAMPLE a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4, so that a(2)  = a(1)*b(0) + 2 = 8 Complement: (b(n)) = (2, 4, 5, 6, 7, 9, 10, 12, 14, 15, 16, ...) MATHEMATICA mex := First[Complement[Range[1, Max[#1] + 1], #1]] &; a[0] = 1; a[1] = 3; b[0] = 2; b[1] = 4; a[n_] := a[n] = a[n - 1]*b[n - 2] + n; b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]]; Table[a[n], {n, 0, 40}]  (* A294385 *) Table[b[n], {n, 0, 10}] CROSSREFS Cf. A293076, A293765, A294381. Sequence in context: A226679 A216541 A194090 * A020099 A182392 A005635 Adjacent sequences:  A294382 A294383 A294384 * A294386 A294387 A294388 KEYWORD nonn,more AUTHOR Clark Kimberling, Oct 29 2017 STATUS approved

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Last modified September 21 00:17 EDT 2019. Contains 327252 sequences. (Running on oeis4.)