A022855
a(n) = [ a(n-1)/a(1) ] + [ a(n-1)/a(2) ] + ... + [ a(n-1)/a(n-1) ] for n >= 3, with initial terms 1,1.
Original entry on oeis.org
1, 1, 2, 5, 13, 35, 97, 271, 761, 2143, 6042, 17043, 48081, 135656, 382752, 1079939, 3047074, 8597406, 24257838, 68444231, 193117503, 544886995, 1537415492, 4337865331, 12239421132, 34533905116, 97438480950, 274925686472, 775711324186, 2188693483680, 6175466331563
Offset: 1
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Clear[a]; a[n_] := a[n] = If[n == 1, 1, Sum[Floor[a[n-1]/a[k]], {k, 1, n-1}]]; Table[a[n], {n, 1, 30}] (* Vaclav Kotesovec, May 22 2019 *)
A022874
a(n) = [ a(n-1)/a(1) ] + [ a(n-1)/a(2) ] + ... + [ a(n-1)/a(n-1) ] for n >= 3, with initial terms 2,1.
Original entry on oeis.org
2, 1, 1, 2, 6, 19, 60, 194, 628, 2035, 6597, 21393, 69382, 225031, 729865, 2367255, 7678002, 24902998, 80770936, 261974262, 849693202, 2755914018, 8938593456, 28991634898, 94032120191, 304985891949, 989198096368
Offset: 1
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Clear[a]; a[n_] := a[n] = If[n==1, 2, Sum[Floor[a[n-1]/a[k]], {k, 1, n-1}]]; Table[a[n], {n, 1, 30}] (* Vaclav Kotesovec, May 22 2019 *)
A367787
Let b(0) = 1, b(n) = Sum_{k=0..n-1} b(k) / b(n-k-1), then a(n) is the numerator of b(n).
Original entry on oeis.org
1, 1, 2, 7, 44, 3459, 21398845, 204701870532176, 47683439994850565666251869149, 203292005443961363023193564438853229653319486912062841397
Offset: 0
1, 1, 2, 7/2, 44/7, 3459/308, 21398845/1065372, 204701870532176/5699432573835, ...
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b[0] = 1; b[n_] := b[n] = Sum[b[k]/b[n - k - 1], {k, 0, n - 1}]; a[n_] := Numerator[b[n]]; Table[a[n], {n, 0, 9}]
A367788
Let b(0) = 1, b(n) = Sum_{k=0..n-1} b(k) / b(n-k-1), then a(n) is the denominator of b(n).
Original entry on oeis.org
1, 1, 1, 2, 7, 308, 1065372, 5699432573835, 742435596532024691458409520, 1770094160863794205114840009375146894748207874734794924
Offset: 0
1, 1, 2, 7/2, 44/7, 3459/308, 21398845/1065372, 204701870532176/5699432573835, ...
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b[0] = 1; b[n_] := b[n] = Sum[b[k]/b[n - k - 1], {k, 0, n - 1}]; a[n_] := Denominator[b[n]]; Table[a[n], {n, 0, 9}]
Showing 1-4 of 4 results.
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