%I #15 Feb 21 2024 08:26:18
%S 1,2,2,3,2,3,4,4,4,4,5,4,4,4,5,6,6,4,4,6,6,7,6,7,4,7,6,7,8,8,8,8,8,8,
%T 8,8,9,8,8,8,8,8,8,8,9,10,10,8,8,8,8,8,8,10,10,11,10,11,8,8,8,8,8,11,
%U 10,11,12,12,12,12,8,8,8,8,12,12,12,12,13,12,12,12,13,8,8,8,13,12,12,12,13
%N Array read by antidiagonals: T(n,k) = o(n,k), where o(,) is a binary operation arising from counting the elements that are sums of m squares in a field of characteristic not equal to 2.
%C The array is symmetric (there is an error in the published version of the Allouche-Shallit paper).
%D A. Pfister, Zur Darstellung von -1 als Summe von Quadraten in einem Koerper, J. London Math. Soc. 40 1965 159-165.
%D D. B. Shapiro, Products of sums of squares, Expos. Math., 2 (1984), 235-261.
%H J.-P. Allouche and J. Shallit, <a href="http://www.math.jussieu.fr/~allouche/kreg2.ps">The Ring of k-regular Sequences, II</a> (preprint), ex. 25.
%H J.-P. Allouche and J. Shallit, <a href="https://doi.org/10.1016/S0304-3975(03)00090-2">The ring of k-regular sequences, II</a>, Theoret. Computer Sci., 307 (2003), 3-29.
%H A. Pfister, <a href="https://doi.org/10.1007/BF01389724">Quadratische Formen in beliebigen Körpern</a>, Invent. Math. 1 1966 116-132.
%H D. B. Shapiro, <a href="http://www.math.ohio-state.edu/~shapiro/lec1.pdf">Products of Sums of Squares Lecture 1: Introduction and History</a>
%F T(2m, 2n) = 2T(m, n), T(2m-1, 2n) = 2T(m, n), T(2m, 2n-1) = 2T(m, n), T(2m-1, 2n-1) = 2T(m, n) - (binomial(m+n-2, m-1) mod 2).
%K nonn,tabl
%O 1,2
%A _N. J. A. Sloane_, Oct 01 2003
%E More terms from Pab Ter (pabrlos(AT)yahoo.com), May 27 2004