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A204202 Triangle based on (0,2/3,1) averaging array. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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 * A025124 A030996 A309208

Adjacent sequences:  A204199 A204200 A204201 * A204203 A204204 A204205

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jan 12 2012

STATUS

approved

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Last modified September 21 11:18 EDT 2019. Contains 327253 sequences. (Running on oeis4.)