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

0,4

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".

Links

Reinhard Zumkeller, Rows n = 0..100 of triangle, flattened

BBC, One man went to mow.

Index entries for sequences related to songs

Formula

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

Example

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

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 *)

Prog

(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

Crossrefs

Cf. A193738.

Sequence in context: A237840 A114115 A126268 * A345032 A182535 A181186

Adjacent sequences: A193736 A193737 A193738 * A193740 A193741 A193742

Keyword

nonn,tabl

Author

Clark Kimberling, Aug 04 2011

Status

approved