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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
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

REFERENCES

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

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

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

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, J. Shallit, The Ring of k-regular Sequences, II

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

A. Pfister, Quadratische Formen in beliebigen Koerpern, 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: A249871 A074712 A271914 * A277194 A172151 A106250

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

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Last modified October 17 03:15 EDT 2018. Contains 316275 sequences. (Running on oeis4.)