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A204207
Triangle based on (1,2,3) averaging array.
2
2, 3, 5, 5, 8, 11, 9, 13, 19, 23, 17, 22, 32, 42, 47, 33, 39, 54, 74, 89, 95, 65, 72, 93, 128, 163, 184, 191, 129, 137, 165, 221, 291, 347, 375, 383, 257, 266, 302, 386, 512, 638, 722, 758, 767, 513, 523, 568, 688, 898, 1150, 1360, 1480, 1525, 1535, 1025
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
Cf. A204201.
Sequence in context: A194939 A135635 A238007 * A354704 A287919 A138181
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Jan 12 2012
EXTENSIONS
Example corrected by Philippe Deléham, Dec 22 2013
STATUS
approved