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A070879
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Stern's diatomic array read by rows (version 3 - same as version 2, A070878, but with final 0 in each row omitted).
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6
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1, 1, 1, 1, 2, 1, 1, 1, 3, 2, 3, 1, 2, 1, 1, 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1, 1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1, 1, 6, 5, 9, 4, 11, 7, 10, 3, 11, 8, 13, 5, 12, 7, 9, 2, 9, 7, 12, 5, 13, 8, 11, 3, 10, 7, 11, 4, 9, 5, 6, 1, 5, 4, 7, 3, 8
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OFFSET
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0,5
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COMMENTS
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Row n has length 2^n.
The terms (n>0) may be written as a left-justified array with rows of length 2^m:
1,
1, 1,
1, 2, 1, 1,
1, 3, 2, 3, 1, 2, 1, 1,
1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1,
1, 5, 4, 7, 3, 8, 5, 7, 2, 7, 5, 8, 3, 7, 4, 5, 1, 4, 3, 5, 2, 5, 3, 4,...
as well as right-justified fashion:
1,
1, 1,
1, 2, 1, 1,
1, 3, 2, 3, 1, 2, 1, 1,
1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1,
... , 2, 7, 5, 8, 3, 7, 4, 5, 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, 2, 1, 1,
...
For properties see FORMULA section.
(End)
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LINKS
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FORMULA
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a(2^(m+1)+k-1) = A002487(2^m+k); a(2^(m+1)+2^m+k-1) = a(2^m+k-1) for m >= 0, 0 <= k < 2^m.
a(2^(m+1)-1-(k+1)) = A002487(k+1); a(2^(m+1)+k) - a(2^m+k) = A002487(k) for m >= 0, 0 <= k < 2^m.
a(2^m-1) = 1 for m >= 0; a(2^(m+1)+k-1) = a(2^(m+1)-k-1) + a(2^m+k-1) for m >= 0, 0 < k < 2^m.
a(2^m+2^m'+k'-1) = a(2^(m'+1)+k'-1)*(m-m'-1) + a(2^m'+k'-1) for m >= 1, 0 <= m' < m, 0 <= k' < 2^m'.
(End)
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CROSSREFS
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KEYWORD
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nonn,tabf,easy
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AUTHOR
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EXTENSIONS
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More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 07 2003
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STATUS
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approved
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