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 A296217 Solution of the complementary equation a(n) = a(1)*b(n-2) + a(2)*b(n-3) + ... + a(n-1)*b(0), where a(0) = 1, a(1) = 2, b(0) = 3, and (a(n)) and (b(n)) are increasing complementary sequences. 4
 1, 2, 6, 26, 112, 484, 2088, 9008, 38862, 167658, 723308, 3120486, 13462360, 58079138, 250564260, 1080981064, 4663554414, 20119445656, 86799050160, 374467330636, 1615522076050, 6969664279584, 30068434774274, 129720849313094, 559639996988064, 2414391579204576 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The increasing complementary sequences a() and b() are uniquely determined by the titular equation and initial values. See A295862 for a guide to related sequences. LINKS Clark Kimberling, Complementary equations, J. Int. Seq. 19 (2007), 1-13. EXAMPLE a(0) =1, a(1) = 2, b(0) = 3, b(1) = 4, b(2) = 4 a(2) = a(1)*b(0) = 2 Complement: (b(n)) = (3, 4, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, ...) MATHEMATICA a = 1; a = 2; b = 3; a[n_] := a[n] = Sum[a[k]*b[n - k - 1], {k, 1, n - 1}]; b[n_] := b[n] = mex[Flatten[Table[Join[{a[n]}, {a[i], b[i]}], {i, 0, n - 1}]]]; u = Table[a[n], {n, 0, 200}];  (* A296217 *) Table[b[n], {n, 0, 20}] N[Table[a[n]/a[n - 1], {n, 1, 200, 10}], 200]; RealDigits[Last[t], 10][] (* A296218 *) CROSSREFS Cf. A296000, A296218. Sequence in context: A192403 A282618 A192435 * A050890 A114710 A230245 Adjacent sequences:  A296214 A296215 A296216 * A296218 A296219 A296220 KEYWORD nonn,easy AUTHOR Clark Kimberling, Dec 08 2017 STATUS approved

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Last modified October 20 02:54 EDT 2019. Contains 328244 sequences. (Running on oeis4.)