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Row sums of A119687.
2

%I #21 Mar 19 2024 10:25:40

%S 1,2,4,12,104,7708,42181224,1259630774324312,

%T 1123743023025850233599250718672,

%U 893151516212832508883674101518508312952543518197504822363196

%N Row sums of A119687.

%F a(n) = Sum_{k=0..n} T(n, k) where T(n, k) = T(n-1, k-1)^2 + T(n-1, k)^2; T(0,0)=1; T(n,-1):=0; T(n, k):=0, n < k.

%e 1 = 1;

%e 1 + 1 = 2;

%e 1 + 2 + 1 = 4;

%e 1 + 5 + 5 + 1 = 12.

%o (Python)

%o def r(i):

%o t = [[0, 1, 0], [0, 1, 1, 0]]

%o for n in range(2, i+1):

%o t.append([0])

%o for k in range(1, n+2):

%o t[n].append(t[n-1][k-1]**2 + t[n-1][k]**2)

%o t[n].append(0)

%o return(sum(t[i]))

%o for n in range(1, 10):

%o print (r(n))

%Y Cf. A119687.

%K nonn

%O 1,2

%A _Cortney Reagle_, Sep 17 2019

%E a(10) corrected by _Georg Fischer_, Mar 19 2024