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A193738 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. 6
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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

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

LINKS

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

EXAMPLE

First six rows:

1

1....1

1....2....2

1....2....3....3

1....2....3....4...4

1....2....3....4...5...5

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. A193722, A193739.

Sequence in context: A070680 A054711 A241424 * A230494 A134658 A106580

Adjacent sequences:  A193735 A193736 A193737 * A193739 A193740 A193741

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Aug 04 2011

STATUS

approved

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Last modified December 8 21:06 EST 2016. Contains 278956 sequences.