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Search: id:A087735
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| A087735 |
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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. |
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+0
1
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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The array is symmetric (there is an error in the published version of the Allouche-Shallit paper).
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REFERENCES
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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.
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LINKS
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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
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FORMULA
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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).
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CROSSREFS
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Adjacent sequences: A087732 A087733 A087734 this_sequence A087736 A087737 A087738
Sequence in context: A123229 A127095 A074712 this_sequence A106250 A029248 A085916
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KEYWORD
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nonn,tabl
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AUTHOR
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njas, Oct 01 2003
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EXTENSIONS
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More terms from Pab Ter (pabrlos(AT)yahoo.com), May 27 2004
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