A128221 A128174 * A127701.

1, 1, 2, 1, 1, 3, 1, 2, 1, 4, 1, 1, 3, 1, 5, 1, 2, 1, 4, 1, 6, 1, 1, 3, 1, 5, 1, 7, 1, 2, 1, 4, 1, 6, 1, 8, 1, 1, 3, 1, 5, 1, 7, 1, 9, 1, 2, 1, 4, 1, 6, 1, 8, 1, 10, 1, 1, 3, 1, 5, 1, 7, 1, 9, 1, 11, 1, 2, 1, 4, 1, 6, 1, 8, 1, 10, 1, 12, 1, 1, 3, 1, 5, 1, 7, 1, 9, 1, 11, 1, 13

Offset: 1

Author

Gary W. Adamson, Feb 19 2007

Keywords

• nonn
• tabl

Comments

Row sums = A024206: (1, 3, 5, 8, 11, 15, 19, ...). A128222 = A127701 * A128174.

Table T(n,k) = n, if k is odd, 1 if k is even; n, k > 0, read by antidiagonals. -Boris Putievskiy, Jan 30 2013

Examples

			From _Boris Putievskiy_, Jan 30 2013: (Start)
The start of the sequence as a table:
  1, 1, 1, 1, 1, 1, 1, ...
  2, 1, 2, 1, 2, 1, 2, ...
  3, 1, 3, 1, 3, 1, 3, ...
  4, 1, 4, 1, 4, 1, 4, ...
  5, 1, 5, 1, 5, 1, 5, ...
  6, 1, 6, 1, 6, 1, 6, ...
  7, 1, 7, 1, 7, 1, 7, ...
  ...
(End)
First few rows of the triangle are:
  1;
  1, 2;
  1, 1, 3;
  1, 2, 1, 4;
  1, 1, 3, 1, 5;
  1, 2, 1, 4, 1, 6;
  1, 1, 3, 1, 5, 1, 7;
  ...
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A128174, A127701, A024206, A128222.

Programs

Mathematica

a128221[n_, k_] := If[EvenQ[n-k], k, 1]/;1<=k<=n
a128221[r_] := Table[a128221[n, k], {n, 1, r}, {k, 1, n}]
TableForm[a128221[7]] (* triangle *)
Flatten[a128221[10]] (* data *) (* Hartmut F. W. Hoft, Mar 08 2017 *)
t[r_, c_] := If[ OddQ@ c, r, 1]; Table[t[k, n - k + 1], {n, 13}, {k, n}] // Flatten (* Robert G. Wilson v, Mar 09 2017 *)

Formula

A128174 * A127701 as infinite lower triangular matrices. By columns, k-th column = k, 1, k, ...; k=1,2,3,...

From Boris Putievskiy, Jan 30 2013: (Start)

As table T(n,k) = (1+(-1)^k)/2 - (-1+(-1)^k)*n/2.

As linear sequence a(n) = (1+(-1)^A004736(n))/2 - (-1+(-1)^A004736(n))*A002260(n)/2. a(n) = (1+(-1)^j)/2 - (-1+(-1)^j)*i/2,

where i = n-t*(t+1)/2, j = (t*t+3*t+4)/2-n, t=floor((-1+sqrt(8*n-7))/2). (End)

Extensions

More terms from Robert G. Wilson v, Mar 09 2017