cp's OEIS Frontend

A204203 Triangle based on (0,1/4,1) averaging array.

%I A204203 #9 Dec 24 2013 01:53:29
%S A204203 1,1,5,1,6,13,1,7,19,29,1,8,26,48,61,1,9,34,74,109,125,1,10,43,108,
%T A204203 183,234,253,1,11,53,151,291,417,487,509,1,12,64,204,442,708,904,996,
%U A204203 1021,1,13,76,268,646,1150,1612,1900,2017,2045,1,14,89,344,914
%N A204203 Triangle based on (0,1/4,1) averaging array.
%C A204203 See A204201 for a discussion and guide to other averaging arrays.
%F A204203 From _Philippe Deléham_, Dec 24 2013: (Start)
%F A204203 T(n,n) = A036563(n+1).
%F A204203 Sum_{k=1..n} T(n,k) = A014480(n-1).
%F A204203 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)=5, T(n,k)=0 if k<1 or if k>n. (End)
%e A204203 First six rows:
%e A204203 1
%e A204203 1...5
%e A204203 1...6...13
%e A204203 1...7...19...29
%e A204203 1...8...26...48...61
%e A204203 1...9...34...74...109...125
%t A204203 a = 0; r = 1/4; b = 1;  t[1, 1] = r;
%t A204203 t[n_, 1] := (a + t[n - 1, 1])/2;
%t A204203 t[n_, n_] := (b + t[n - 1, n - 1])/2;
%t A204203 t[n_, k_] := (t[n - 1, k - 1] + t[n - 1, k])/2;
%t A204203 u[n_] := Table[t[n, k], {k, 1, n}]
%t A204203 Table[u[n], {n, 1, 5}]    (* averaging array *)
%t A204203 u = Table[(1/2) (1/r) 2^n*u[n], {n, 1, 12}];
%t A204203 TableForm[u]  (* A204203 triangle *)
%t A204203 Flatten[u]    (* A204203 sequence *)
%Y A204203 Cf. A204201.
%K A204203 nonn,tabl
%O A204203 1,3
%A A204203 _Clark Kimberling_, Jan 12 2012