A327563 Row sums of A119687.

1, 2, 4, 12, 104, 7708, 42181224, 1259630774324312, 1123743023025850233599250718672, 893151516212832508883674101518508312952543518197504822363196

Offset: 1

Author

Cortney Reagle, Sep 17 2019

Keywords

• nonn

Examples

			1 = 1;
1 + 1 = 2;
1 + 2 + 1 = 4;
1 + 5 + 5 + 1 = 12.
		

Crossrefs

Cf. A119687.

Programs

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