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

1,3

Comments

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

Links

Table of n, a(n) for n=1..59.

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

Example

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

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 *)

Crossrefs

Cf. A204201.

Sequence in context: A082830 A261622 A046902 * A143019 A337369 A156921

Adjacent sequences: A204202 A204203 A204204 * A204206 A204207 A204208

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 12 2012

Status

approved