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A298352
a(n) = a(n-1) + a(n-2) + a([(n-1)/2]), where a(0) = 1, a(1) = 1, a(2) = 1.
2
1, 1, 1, 3, 5, 9, 15, 27, 45, 77, 127, 213, 349, 577, 941, 1545, 2513, 4103, 6661, 10841, 17579, 28547, 46253, 75013, 121479, 196841, 318669, 516087, 835333, 1352361, 2188635, 3542541, 5732721, 9277775, 15013009, 24294887, 39311999, 63613547, 102932207
OFFSET
0,4
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
MATHEMATICA
a[0] = 1; a[1] = 1; a[2] = 1;
a[n_] := a[n] = a[n - 1] + a[n - 2] + a[Floor[(n-1)/2]];
Table[a[n], {n, 0, 30}] (* A298352 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 10 2018
STATUS
approved