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 A294382 Solution of the complementary equation a(n) = a(n-1)*b(n-2) - 1, where a(0) = 1, a(1) = 3, b(0) = 2, b(1) = 4. 2
 1, 3, 5, 19, 113, 790, 6319, 56870, 568699, 6255688, 75068255, 975887314, 13662422395 (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) - 1 = 5 Complement: (b(n)) = (2, 4, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, ...) MATHEMATICA mex := First[Complement[Range[1, Max[#1] + 1], #1]] &; a = 1; a = 3; b = 2; b = 4; a[n_] := a[n] = a[n - 1]*b[n - 2] - 1; b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]]; Table[a[n], {n, 0, 40}]  (* A294382 *) Table[b[n], {n, 0, 10}] CROSSREFS Cf. A293076, A293765, A294381. Sequence in context: A055452 A184254 A077458 * A201108 A291920 A172058 Adjacent sequences:  A294379 A294380 A294381 * A294383 A294384 A294385 KEYWORD nonn,more AUTHOR Clark Kimberling, Oct 29 2017 STATUS approved

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Last modified January 26 16:21 EST 2021. Contains 340442 sequences. (Running on oeis4.)