A128022 -id:A128022 - cp's OEIS frontend

A128023 a(n) = A128022(n)/n.

1, 1, 1, 2, 3, 5, 9, 16, 28, 51, 92, 169, 312, 580, 1082, 2029, 3819, 7214, 13669, 25971, 49468, 94439, 180666, 346277, 664852, 1278561, 2462414, 4748941, 9170369, 17729380, 34314929, 66485175, 128940946, 250297130, 486291567, 945566936

Offset: 1

Leroy Quet, Feb 11 2007

Cf. A128022.

f[l_List] := Block[{n = Length[l] + 1},Append[l, Ceiling[Sum[k*l[[k]], {k, n - 1}]/n]]];Nest[f, {1}, 36] (* Ray Chandler, Feb 12 2007 *)

a(1)=1, a(n) = ceiling(Sum_{k=1..n-1} A128022(k)/n).

Extended by Ray Chandler, Feb 12 2007

A128020 a(n) = the multiple of n which is > (sum{k=1 to n-1} a(k)) and is <= (n + sum{k=1 to n-1} a(k)).

Original entry on oeis.org

1, 2, 6, 12, 25, 48, 98, 200, 396, 790, 1584, 3168, 6331, 12670, 25335, 50672, 101354, 202698, 405403, 810800, 1621599, 3243196, 6486391, 12972792, 25945575, 51891164, 103782330, 207564644, 415129287, 830258580, 1660517170, 3321034336

Offset: 1

Leroy Quet, Feb 11 2007

Cf. A128021, A128022.

f[l_List] := Block[{n = Length[l] + 1},Append[l, n*(1 + Floor[Plus @@ l/n])]];Nest[f, {}, 33] (* Ray Chandler, Feb 12 2007 *)

a(n) = n * (1+ floor(sum{k=1 to n-1} a(k) /n)).

Extended by Ray Chandler, Feb 12 2007

A129571 A129360 * A007318.

Original entry on oeis.org

1, 1, 1, 0, 2, 1, 1, 3, 3, 1, 0, 4, 6, 4, 1, 0, 4, 10, 10, 5, 1, 0, 6, 15, 20, 15, 6, 1, 1, 7, 21, 35, 35, 21, 7, 1, 0, 6, 27, 56, 70, 56, 28, 8, 1, 0, 8, 36, 84, 126, 126, 84, 36, 9, 1

Offset: 1

Gary W. Adamson, Apr 22 2007

First 10 row sums match A128022: (1, 2, 3, 8, 15, 30, 63, 128, 252, 510, ...). A129570 = A007318 * A129360.

			First few rows of the triangle:
  1;
  1,  1;
  0,  2,  1;
  1,  3,  3,  1;
  0,  4,  6,  4,  1;
  0,  4, 10, 10,  5,  1;
  0,  6, 15, 20, 15,  6,  1;
  1,  7, 21, 35, 35, 21,  7,  1;
  ...

Cf. A007318, A129360, A128022, A129570.

A129360 * A007318 as infinite lower triangular matrices.

cp's OEIS Frontend

A128023 a(n) = A128022(n)/n.

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A128020 a(n) = the multiple of n which is > (sum{k=1 to n-1} a(k)) and is <= (n + sum{k=1 to n-1} a(k)).

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Mathematica

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A129571 A129360 * A007318.

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