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 A297831 Solution of the complementary equation a(n) = a(1)*b(n-1) - a(0)*b(n-2) + 2*n - 1, 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. 3
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 OFFSET 0,2 COMMENTS 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. Conjecture: a(n) - (2 +sqrt(2))*n < 5/2 for n >= 1. LINKS Clark Kimberling, Table of n, a(n) for n = 0..10000 EXAMPLE a(0) = 1, a(1) = 2, b(0) = 3, b(1) = 4, so that a(2) = 8. Complement: (b(n)) = (3,4,5,6,7,9,10,12,13,15,16,18,19,...) MATHEMATICA a[0] = 1; a[1] = 2; b[0] = 3; b[1] = 4; a[n_] := a[n] = a[1]*b[n - 1] - a[0]*b[n - 2] + 2 n - 1; j = 1; While[j < 100, k = a[j] - j - 1; While[k < a[j + 1] - j + 1, b[k] = j + k + 2; k++]; j++]; k Table[a[n], {n, 0, k}] (* A297831 *) CROSSREFS Cf. A297826, A297830. Sequence in context: A216538 A077820 A360649 * A045086 A064105 A129516 Adjacent sequences: A297828 A297829 A297830 * A297832 A297833 A297834 KEYWORD nonn,easy AUTHOR Clark Kimberling, Feb 04 2018 STATUS approved

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Last modified October 4 22:44 EDT 2023. Contains 365888 sequences. (Running on oeis4.)