A204205 Triangle based on (0,1/5,1) averaging array.

1, 1, 6, 1, 7, 16, 1, 8, 23, 36, 1, 9, 31, 59, 76, 1, 10, 40, 90, 135, 156, 1, 11, 50, 130, 225, 291, 316, 1, 12, 61, 180, 355, 516, 607, 636, 1, 13, 73, 241, 535, 871, 1123, 1243, 1276, 1, 14, 86, 314, 776, 1406, 1994, 2366, 2519, 2556, 1, 15, 100, 400

Offset: 1

Author

Clark Kimberling, Jan 12 2012

Keywords

• nonn
• tabl

Comments

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

Examples

			First six rows:
1
1...6
1...7...16
1...8...23...36
1...9...31...59...76
1...10..40...90...135...156
		

Crossrefs

Cf. A204201.

Programs

Mathematica

a = 0; r = 1/5; 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[(1/2) (1/r) 2^n*u[n], {n, 1, 12}];
TableForm[u]   (* A204205 triangle *)
Flatten[u]     (* A204205 sequence *)

Formula

T(n,n) = A048487(n-1). - 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)=1, T(2,1)=1, T(2,2)=6, T(n,k)=0 if k<1 or if k>n. - Philippe Deléham, Dec 24 2013