A174829 An averaging sum sequence based on( improved):a(n,m,q)=Floor[(a(n - 1, m - 1,q) + a(n - 1, m,q))/2] with limit q

1, 1, 2, 1, 3, 4, 1, 4, 6, 7, 1, 5, 7, 9, 11, 1, 6, 9, 12, 14, 16, 1, 7, 10, 13, 16, 19, 21, 1, 8, 12, 15, 18, 21, 24, 27, 1, 9, 13, 17, 21, 24, 27, 30, 33, 1, 10, 15, 20, 25, 28, 32, 35, 39, 42, 1, 11, 16, 21, 26, 30, 34, 38, 42, 46, 50, 1, 12, 18, 23, 28, 33, 38, 42, 46, 50, 54, 58

Offset

0,3

Comments

Row sums are:

{1, 3, 8, 18, 33, 58, 87, 126, 175, 247, 315, 403, 510,...}.

First Mathematica version of this sequence didn't average right for q levels.

Example a(n,m) for q=10:

{1},

{1, 10},

{1, 5, 10},

{1, 3, 7, 10},

{1, 2, 5, 8, 10},

{1, 1, 3, 6, 9, 10},

{1, 1, 2, 4, 7, 9, 10},

{1, 1, 1, 3, 5, 8, 9, 10},

{1, 1, 1, 2, 4, 6, 8, 9, 10},

{1, 1, 1, 1, 3, 5, 7, 8, 9, 10},

{1, 1, 1, 1, 2, 4, 6, 7, 8, 9, 10}

Links

Table of n, a(n) for n=0..77.

Formula

a(n,m,q)=Floor[(a(n - 1, m - 1,q) + a(n - 1, m,q))/2] with limit q:

t(n,q)=Sum(a(n,m,q),{m,0,q}]

Example

{1},
{1, 2},
{1, 3, 4},
{1, 4, 6, 7},
{1, 5, 7, 9, 11},
{1, 6, 9, 12, 14, 16},
{1, 7, 10, 13, 16, 19, 21},
{1, 8, 12, 15, 18, 21, 24, 27},
{1, 9, 13, 17, 21, 24, 27, 30, 33},
{1, 10, 15, 20, 25, 28, 32, 35, 39, 42},
{1, 11, 16, 21, 26, 30, 34, 38, 42, 46, 50},
{1, 12, 18, 23, 28, 33, 38, 42, 46, 50, 54, 58},
{1, 13, 19, 25, 31, 37, 42, 47, 51, 55, 59, 63, 67}

Mathematica

a[0, 0, q_] := 1; a[1, 0, q_] := 1; a[1, 1, q_] = q;
a[n_, 0, q_] := 1; a[n_, n_, q_] := q;
a[n_, m_, q_] := a[n, m, q] = Floor[(a[n - 1, m - 1, q] + a[n - 1, m, q])/2]
Table[Table[Sum[a[n, m, q], {m, 0, n}], {n, 0, q}], {q, 0, 12}];
Flatten[%]

Crossrefs

Sequence in context: A174828 A305309 A085643 * A132110 A039912 A163311

Adjacent sequences: A174826 A174827 A174828 * A174830 A174831 A174832

Keyword

nonn,tabl,uned

Author

Roger L. Bagula, Mar 30 2010

Status

approved