A204206 Triangle based on (1,3/2,2) averaging array.

3, 5, 7, 9, 12, 15, 17, 21, 27, 31, 33, 38, 48, 58, 63, 65, 71, 86, 106, 121, 127, 129, 136, 157, 192, 227, 248, 255, 257, 265, 293, 349, 419, 475, 503, 511, 513, 522, 558, 642, 768, 894, 978, 1014, 1023, 1025, 1035, 1080, 1200, 1410, 1662, 1872

Offset

1,1

Comments

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

Links

Table of n, a(n) for n=1..52.

Formula

From Philippe Deléham, Dec 24 2013: (Start)

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

Sum_{k=1..n} T(n,k) = A167667(n).

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)=5, T(2,2)=7, T(n,k)=0 if k<1 or if k>n. (End)

Example

First six rows:
3
5...7
9...12...15
17..21...27...31
33..38...48...58...63
65..71...86...106..121..127

Mathematica

a = 1; r = 3/2; b = 2;
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]   (* A204206 triangle *)
Flatten[u]     (* A204206 sequence *)

Crossrefs

Cf. A204201.

Sequence in context: A072154 A309269 A362135 * A080751 A025218 A258782

Adjacent sequences: A204203 A204204 A204205 * A204207 A204208 A204209

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 12 2012

Status

approved