A176809 Triangle read by rows: T(n,m) = 1 - (ceiling((n-1)/m) + ceiling((n-1)/(n-m+1))) + ceiling((n-1)/1) + ceiling((n-1)/(n-1+1)).

1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 2, 3, 1, 1, 3, 3, 3, 3, 1, 1, 4, 4, 4, 4, 4, 1, 1, 4, 4, 5, 5, 4, 4, 1, 1, 5, 5, 6, 6, 6, 5, 5, 1, 1, 5, 6, 6, 7, 7, 6, 6, 5, 1, 1, 6, 6, 7, 8, 8, 8, 7, 6, 6, 1, 1, 6, 7, 8, 8, 9, 9, 8, 8, 7, 6, 1, 1, 7, 8, 9, 9, 10, 10, 10, 9, 9, 8, 7, 1

Offset

1,5

Comments

Row sums are {1, 2, 4, 6, 10, 14, 22, 28, 40, 50, ...}.

Links

Table of n, a(n) for n=1..91.

Formula

T(n,m) = 1 - (ceiling((n-1)/m) + ceiling((n-1)/(n-m+1))) + ceiling((n-1)/1) + ceiling((n-1)/(n-1+1)).

Example

{1},
{1, 1},
{1, 2, 1},
{1, 2, 2, 1},
{1, 3, 2, 3, 1},
{1, 3, 3, 3, 3, 1},
{1, 4, 4, 4, 4, 4, 1},
{1, 4, 4, 5, 5, 4, 4, 1},
{1, 5, 5, 6, 6, 6, 5, 5, 1},
{1, 5, 6, 6, 7, 7, 6, 6, 5, 1}

Mathematica

t[n_, m_] = 1 - (Ceiling[(n - 1)/m] + Ceiling[(n - 1)/(n - m + 1)]) + Ceiling[(n - 1)/1] + Ceiling[(n - 1)/(n - 1 + 1)];
Table[Table[t[n, m], {m, 1, n}], {n, 1, 10}];
Flatten[%]

Crossrefs

Cf. A176298.

Sequence in context: A115514 A326038 A122632 * A317815 A318423 A318091

Adjacent sequences: A176806 A176807 A176808 * A176810 A176811 A176812

Keyword

nonn,tabl

Author

Roger L. Bagula, Apr 26 2010

Extensions

Offset corrected by Alois P. Heinz, Jul 04 2019

Status

approved