A204202 Triangle based on (0,2/3,1) averaging array.

2, 2, 5, 2, 7, 11, 2, 9, 18, 23, 2, 11, 27, 41, 47, 2, 13, 38, 68, 88, 95, 2, 15, 51, 106, 156, 183, 191, 2, 17, 66, 157, 262, 339, 374, 383, 2, 19, 83, 223, 419, 601, 713, 757, 767, 2, 21, 102, 306, 642, 1020, 1314, 1470, 1524, 1535, 2, 23, 123, 408, 948

Offset

1,1

Comments

See A204201 for a discussion of averaging arrays and related triangles

Links

Table of n, a(n) for n=1..60.

Formula

From Philippe Deléham, Dec 24 2013: (Start)

T(n,n) = A055010(n) = A083329(n) = A153893(n-1).

Sum_{k=1..n} T(n,k) = A066373(n+1).

T(n,k) = T(n-1,k)+3*T(n-1,k-1)-2*T(n-2,k-1)-2*T(n-2,k-2), T(1,1)=2, T(2,1)=2, T(2,2)=5, T(n,k)=0 if k<1 or if k>n. (End)

Example

First six rows:
2
2...5
2...7....11
2...9....18...23
2...11...27...41...47
2...13...38...68...88..95

Mathematica

a = 0; r = 2/3; b = 1;
t[1, 1] = r;
t[n_, 1] := (a + t[n - 1, 1])/2;
t[n_, n_] := (b + t[n - 1, n - 1])/2;
t[n_, k_] := (t[n - 1, k - 1] + t[n - 1, k])/2;
u[n_] := Table[t[n, k], {k, 1, n}]
Table[u[n], {n, 1, 5}]   (* averaging array *)
u = Table[(1/r) 2^n*u[n], {n, 1, 12}];
TableForm[u]  (* A204202 triangle *)
Flatten[u]    (* A204202 sequence *)

Crossrefs

Cf. A204201.

Sequence in context: A316895 A100030 A029603 * A336924 A025124 A030996

Adjacent sequences: A204199 A204200 A204201 * A204203 A204204 A204205

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 12 2012

Status

approved