OFFSET
1,1
COMMENTS
See A204201 for a discussion and guide to other averaging arrays.
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
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jan 12 2012
STATUS
approved