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A132915
a(0)=0; a(1)=1; a(n) = Sum_{k=1..[sqrt(n)]} a(n-k) for n>=2.
1
0, 1, 1, 1, 2, 3, 5, 8, 13, 26, 47, 86, 159, 292, 537, 988, 1976, 3793, 7294, 14051, 27114, 52252, 100711, 194128, 374205, 748410, 1469706, 2887160, 5673609, 11153090, 21931975, 43115540, 84761374, 166635588, 327597567, 644042044, 1288084088
OFFSET
0,5
COMMENTS
Lim n->infinity {a(n+1)/a(n)} = 2. Contrast with Fibonacci sequence. Also a(n+1)/a(n) = 2 iff n+1 is square.
FORMULA
a(n) = sum a(n-k), k= 1 ... [sqrt(n)] for n>=2; a(0)=0; a(1)=1.
EXAMPLE
a(9) = a(6) + a(7) + a(8) = 5 + 8 + 13 = 26.
CROSSREFS
Cf. A132916.
Sequence in context: A336604 A024318 A324738 * A030036 A115212 A158083
KEYWORD
nonn
AUTHOR
Rick L. Shepherd, Sep 04 2007
STATUS
approved