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 A087735 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. 0

%I

%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 J.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. Computer Sci., 307 (2003), 3-29.

%D A. Pfister, Zur Darstellung von -1 als Summe von Quadraten in einem Koerper, J. London Math. Soc. 40 1965 159-165.

%D A. Pfister, Quadratische Formen in beliebigen Koerpern, Invent. Math. 1 1966 116-132.

%D D. B. Shapiro, Products of sums of squares, Expos. Math., 2 (1984), 235-261.

%H J.-P. Allouche, J. Shallit, <a href="http://www.lri.fr/~allouche/kreg2.ps">The Ring of k-regular Sequences, II</a>

%H J.-P. Allouche, J. Shallit, <a href="http://www.lri.fr/~allouche/kreg2.ps">The Ring of k-regular Sequences, II</a> (preprint), ex. 25.

%H A. Pfister, <a href="http://134.76.163.65/servlet/digbib?template=view.html&amp;id=166640&amp;startpage=132&amp;endpage=148&amp;image-path=http://134.76.176.141/cgi-bin/letgifsfly.cgi&amp;image-subpath=/4229&amp;image-subpath=4229&amp;pagenumber=132&amp;imageset-id=4229">Quadratische Formen in beliebigen Koerpern</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

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