A327563 Row sums of A119687.
1, 2, 4, 12, 104, 7708, 42181224, 1259630774324312, 1123743023025850233599250718672, 893151516212832508883674101518508312952543518197504822363196
Offset: 1
Keywords
Examples
1 = 1; 1 + 1 = 2; 1 + 2 + 1 = 4; 1 + 5 + 5 + 1 = 12.
Crossrefs
Cf. A119687.
Programs
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Python
def r(i): t = [[0, 1, 0], [0, 1, 1, 0]] for n in range(2, i+1): t.append([0]) for k in range(1, n+2): t[n].append(t[n-1][k-1]**2 + t[n-1][k]**2) t[n].append(0) return(sum(t[i])) for n in range(1, 10): print (r(n))
Formula
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.
Extensions
a(10) corrected by Georg Fischer, Mar 19 2024