%I #9 Dec 25 2013 02:30:45
%S 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,
%T 225,291,316,1,12,61,180,355,516,607,636,1,13,73,241,535,871,1123,
%U 1243,1276,1,14,86,314,776,1406,1994,2366,2519,2556,1,15,100,400
%N Triangle based on (0,1/5,1) averaging array.
%C See A204201 for a discussion and guide to other averaging arrays.
%F T(n,n) = A048487(n-1). - _Philippe Deléham_, Dec 24 2013
%F 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
%e First six rows:
%e 1
%e 1...6
%e 1...7...16
%e 1...8...23...36
%e 1...9...31...59...76
%e 1...10..40...90...135...156
%t a = 0; r = 1/5; b = 1;
%t t[1, 1] = r;
%t t[n_, 1] := (a + t[n - 1, 1])/2;
%t t[n_, n_] := (b + t[n - 1, n - 1])/2;
%t t[n_, k_] := (t[n - 1, k - 1] + t[n - 1, k])/2;
%t u[n_] := Table[t[n, k], {k, 1, n}]
%t Table[u[n], {n, 1, 5}] (* averaging array *)
%t u = Table[(1/2) (1/r) 2^n*u[n], {n, 1, 12}];
%t TableForm[u] (* A204205 triangle *)
%t Flatten[u] (* A204205 sequence *)
%Y Cf. A204201.
%K nonn,tabl
%O 1,3
%A _Clark Kimberling_, Jan 12 2012
|