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 A298403 a(n) = 2*a(n-1) - a(n-3) + a(floor(n/2)), where a(0) = 1, a(1) = 2, a(2) = 3. 3
 1, 2, 3, 7, 15, 30, 60, 112, 209, 373, 664, 1149, 1985, 3366, 5695, 9517, 15877, 26268, 43392, 71280, 116956, 191184, 312237, 508667, 828135, 1346018, 2186735, 3548701, 5757079, 9333118, 15127052, 24506542, 39695843, 64280511, 104080748, 168491921, 272746723 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n)/a(n-1) -> (1 + sqrt(5))/2, the golden ratio (A001622), so that (a(n)) has the growth rate of the Fibonacci numbers (A000045). See A298338 for a guide to related sequences. LINKS Clark Kimberling, Table of n, a(n) for n = 0..1000 MATHEMATICA a[0] = 1; a[1] = 2; a[2] = 3; a[n_] := a[n] = 2*a[n - 1] - a[n - 3] + a[Floor[n/2]]; Table[a[n], {n, 0, 90}]  (* A298403 *) CROSSREFS Cf. A001622, A000045, A298338, A298402. Sequence in context: A074742 A020873 A049958 * A177487 A153010 A076993 Adjacent sequences:  A298400 A298401 A298402 * A298404 A298405 A298406 KEYWORD nonn,easy AUTHOR Clark Kimberling, Feb 10 2018 STATUS approved

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Last modified December 8 20:37 EST 2021. Contains 349596 sequences. (Running on oeis4.)