OFFSET
1,1
COMMENTS
See A204201 for a discussion and guide to other averaging arrays.
FORMULA
T(n,n) = A083329(n). - Philippe Deléham, Dec 24 2013
T(n,1) = A000051(n-1). - Philippe Deléham, Dec 24 2013
Sum_{k=1..n} T(n,k)=A036289(n). - Philippe Deléham, Dec 24 2013
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)=3, T(2,2)=5, T(n,k)=0 if k<1 or if k>n. - Philippe Deléham, Dec 24 2013
EXAMPLE
First six rows:
2
3....5
5....8....11
9....13...19...23
17...22...32...42...47
33...39...54...74...89...95
MATHEMATICA
a = 1; r = 2; b = 3;
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[2 (1/2) (1/r) 2^n*u[n], {n, 1, 12}];
TableForm[u] (* A204207 triangle *)
Flatten[u] (* A204207 sequence *)
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jan 12 2012
EXTENSIONS
Example corrected by Philippe Deléham, Dec 22 2013
STATUS
approved