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%I #6 Apr 03 2024 19:14:29
%S 0,1,4,5,9,16,28,17,29,52,37,60,72,73,85,88,121,140,145,97,136,113,
%T 137,208,180,216,165,181,156,228,201,241,252,249,276,249,284,321,293,
%U 348,305,392,373,408,404,337,385,441,449,460,456,461,476,461,488,505
%N a(n) is the number of 0's in a p X p square of a particular function mod p (see Formula) where p is the n-th prime.
%C Original name: Related to Lucas property of a number array.
%C Corresponds to the numbers z(1|1,1,1) in Razpet, Table 4, p. 163 (but note Razpet has an error for p=23). - _Sean A. Irvine_, Apr 03 2024
%D M. Razpet, The Lucas property of a number array, Discrete Math., 248 (2002), 157-168.
%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a069/A069089.java">Java program</a> (github)
%F Let p be the n-th prime and w(i,j) = Sum_{k=max(i,j)..i+j} binomial(k, i) * binomial(i, k - j), then a(n) is the number of values w(i,j) = 0 (mod p) in the square bounded by 0<=i,j<p [see Razpet p. 159 for a more general w function].
%K nonn
%O 1,3
%A _N. J. A. Sloane_, Apr 12 2002
%E a(9) corrected and more terms from _Sean A. Irvine_, Apr 03 2024