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A298349
a(n) = a(n-1) + a(n-2) + a([(n+1)/2]), where a(0) = 1, a(1) = 2, a(2) = 3.
2
1, 2, 3, 8, 14, 30, 52, 96, 162, 288, 480, 820, 1352, 2268, 3716, 6146, 10024, 16458, 26770, 43708, 70958, 115486, 187264, 304102, 492718, 799088, 1294074, 2096878, 3394668, 5497692, 8898506, 14406222, 23314752, 37737432, 61068642, 98832844, 159928256
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+1)/2]];
Table[a[n], {n, 0, 30}] (* A298349 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 10 2018
STATUS
approved