A171001 Binomial(n-k,k)^2 where k = ceiling(n/4).
1, 0, 1, 4, 9, 9, 36, 100, 225, 400, 1225, 3136, 7056, 15876, 44100, 108900, 245025, 627264, 1656369, 4008004, 9018009, 25050025, 64128064, 153165376, 344622096, 1012766976, 2538950544, 6009350400, 13521038400, 41408180100, 102252852900, 240407818596
Offset: 0