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A298402
a(n) = 2*a(n-1) - a(n-3) + a(floor(n/2)), where a(0) = 1, a(1) = 1, a(2) = 1.
3
1, 1, 1, 2, 4, 8, 16, 30, 56, 100, 178, 308, 532, 902, 1526, 2550, 4254, 7038, 11626, 19098, 31336, 51224, 83658, 136288, 221884, 360642, 585898, 950814, 1542512, 2500652, 4053040, 6566118, 10635838, 17222890, 27886700, 45144600, 73077936, 118280798
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] = 2*a[n - 1] - a[n - 3] + a[Floor[n/2]];
Table[a[n], {n, 0, 90}] (* A298402 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Feb 10 2018
STATUS
approved