A204204 Triangle based on (0,3/4,1) averaging array.

3, 3, 7, 3, 10, 15, 3, 13, 25, 31, 3, 16, 38, 56, 63, 3, 19, 54, 94, 119, 127, 3, 22, 73, 148, 213, 246, 255, 3, 25, 95, 221, 361, 459, 501, 511, 3, 28, 120, 316, 582, 820, 960, 1012, 1023, 3, 31, 148, 436, 898, 1402, 1780, 1972, 2035, 2047, 3, 34, 179

Offset

1,1

Comments

See A204201 for a discussion and guide to other averaging arrays.

Links

Table of n, a(n) for n=1..58.

Formula

From Philippe Deléham, Dec 24 2013: (Start)

T(n,n) = A000225(n+1).

Sum_{k=1..n} T(n,k) = A128135(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)=3, T(2,1)=3, T(2,2)=7, T(n,k)=0 if k<1 or if k>n. (End)

Example

First six rows:
3
3...7
3...10...15
3...13...25...31
3...16...38...56...63
3...19...54...94...119..127

Mathematica

a = 0; r = 3/4; 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[3 (1/2) (1/r) 2^n*u[n], {n, 1, 12}];
TableForm[u]  (* A204204 triangle *)
Flatten[u]    (* A204204 sequence *)

Crossrefs

Cf. A204201.

Sequence in context: A092693 A134661 A135434 * A164928 A253249 A069949

Adjacent sequences: A204201 A204202 A204203 * A204205 A204206 A204207

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 12 2012

Status

approved