A193739 Mirror of the triangle A193738.

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

Offset: 0

Author

Clark Kimberling, Aug 04 2011

Keywords

• nonn
• tabl

Comments

This sequence is obtained by reversing the rows of the triangle A193738.

Except for the first term, this sequence gives the integers occurring in the song "One man went to mow".

Examples

			First six rows:
1
1....1
2....2....1
3....3....2....1
4....4....3....2...1
5....5....4....3...2...1
		

Links

• Reinhard Zumkeller, Rows n = 0..100 of triangle, flattened
• BBC, One man went to mow.
• Index entries for sequences related to songs

Crossrefs

Cf. A193738.

Programs

Haskell

a193738 n k = a193738_tabl !! n !! k
a193738_row n = a193738_tabl !! n
a193738_tabl = map reverse a193739_tabl
-- Reinhard Zumkeller, May 11 2013

Mathematica

z = 12;
p[0, x_] := 1
p[n_, x_] := x*p[n - 1, x] + 1; p[n_, 0] := p[n, x] /. x -> 0
q[n_, x_] := p[n, x]
t[n_, k_] := Coefficient[p[n, x], x^(n - k)];
t[n_, n_] := p[n, x] /. x -> 0;
w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1
g[n_] := CoefficientList[w[n, x], {x}]
TableForm[Table[Reverse[g[n]], {n, -1, z}]]
Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193738 *)
TableForm[Table[g[n], {n, -1, z}]]
Flatten[Table[g[n], {n, -1, z}]]   (* A193739 *)

Formula

Write w(n,k) for the triangle at A193738. The current triangle is then given by w(n,n-k).