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A298341
a(n) = a(n-1) + a(n-2) + a([n/3]), where a(0) = 1, a(1) = 2, a(2) = 3.
2
1, 2, 3, 7, 12, 21, 36, 60, 99, 166, 272, 445, 729, 1186, 1927, 3134, 5082, 8237, 13355, 21628, 35019, 56707, 91786, 148553, 240438, 389090, 629627, 1018883, 1648676, 2667725, 4316673, 6984670, 11301615, 18286730, 29588790, 47875965, 77465484, 125342178
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
MATHEMATICA
a[0] = 1; a[1] = 2; a[2] = 3;
a[n_] := a[n] = a[n - 1] + a[n - 2] + a[Floor[n/3]];
Table[a[n], {n, 0, 30}] (* A298341 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 09 2018
STATUS
approved