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A193739
Mirror of the triangle A193738.
3
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".
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
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Aug 04 2011
STATUS
approved