A193738 - OEIS

%I #8 May 11 2013 18:13:24

%S 1,1,1,1,2,2,1,2,3,3,1,2,3,4,4,1,2,3,4,5,5,1,2,3,4,5,6,6,1,2,3,4,5,6,

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

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

%N Triangular array:  the fusion of polynomial sequences P and Q given by p(n,x)=q(n,x)=x^n+x^(n-1)+...+x+1.

%C See A193722 for the definition of fusion of two sequences of polynomials or triangular arrays.

%H Reinhard Zumkeller, <a href="/A193738/b193738.txt">Rows n = 0..100 of triangle, flattened</a>

%e First six rows:

%e 1

%e 1....1

%e 1....2....2

%e 1....2....3....3

%e 1....2....3....4...4

%e 1....2....3....4...5...5

%t z = 12;

%t p[0, x_] := 1

%t p[n_, x_] := x*p[n - 1, x] + 1; p[n_, 0] := p[n, x] /. x -> 0

%t q[n_, x_] := p[n, x]

%t t[n_, k_] := Coefficient[p[n, x], x^(n - k)];

%t t[n_, n_] := p[n, x] /. x -> 0;

%t w[n_, x_] := Sum[t[n, k]*q[n + 1 - k, x], {k, 0, n}]; w[-1, x_] := 1

%t g[n_] := CoefficientList[w[n, x], {x}]

%t TableForm[Table[Reverse[g[n]], {n, -1, z}]]

%t Flatten[Table[Reverse[g[n]], {n, -1, z}]]  (* A193738 *)

%t TableForm[Table[g[n], {n, -1, z}]]

%t Flatten[Table[g[n], {n, -1, z}]]   (* A193739 *)

%o (Haskell)

%o a193738 n k = a193738_tabl !! n !! k

%o a193738_row n = a193738_tabl !! n

%o a193738_tabl = map reverse a193739_tabl

%o -- _Reinhard Zumkeller_, May 11 2013

%Y Cf. A193722, A193739.

%K nonn,tabl

%O 0,5

%A _Clark Kimberling_, Aug 04 2011