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.

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, 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, 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

Offset

1,2

Comments

The array is symmetric (there is an error in the published version of the Allouche-Shallit paper).

References

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

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

Links

Table of n, a(n) for n=1..91.

J.-P. Allouche and J. Shallit, The Ring of k-regular Sequences, II (preprint), ex. 25.

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

A. Pfister, Quadratische Formen in beliebigen Körpern, Invent. Math. 1 1966 116-132.

D. B. Shapiro, Products of Sums of Squares Lecture 1: Introduction and History

Formula

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).

Crossrefs

Sequence in context: A330408 A074712 A271914 * A322630 A277194 A172151

Adjacent sequences: A087732 A087733 A087734 * A087736 A087737 A087738

Keyword

nonn,tabl

Author

N. J. A. Sloane, Oct 01 2003

Extensions

More terms from Pab Ter (pabrlos(AT)yahoo.com), May 27 2004

Status

approved