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Search: id:A089595
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| A089595 |
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Table T(n,k), n>=0 and k>=0: Stern's diatonic array read by antidiagonals (version 5). |
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1
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| 1, 0, 1, -1, 1, 1, -3, 0, 2, 1, -2, -1, 1, 3, 1, -7, -1, 1, 2, 4, 1, -5, -4, 0, 3, 3, 5, 1, -8, -3, -1, 1, 5, 4, 6, 1, -3, -5, -1, 2, 2, 7, 5, 7, 1, -13, -2, -2, 1, 5, 3, 9, 6, 8, 1, -10, -9, -1, 1, 3, 8, 4, 11, 7, 9, 1, -17, -7, -5, 0, 4, 5, 11, 5, 13, 8, 10, 1, -7, -12, -4, -1, 1, 7, 7, 14, 6, 15, 9, 11, 1, -18, -5, -7, -1, 3, 2, 10, 9, 17, 7
(list; table; graph; listen)
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OFFSET
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0,7
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FORMULA
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Each row is obtained by copying the previous row but interpolating the sum of pairs of adjacent terms.
T(n, 2*k) = T(n-1, k) = T(n, k) - A002487(k).
T(n, 2*k+1) = T(n, 2*k) + T(n, 2*k+2); T(0, 0)=1, T(0, 1)=0.
The k-th column is an arithmetic progression with : T(n, k) = T(0, k) + n* A002487(k).
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EXAMPLE
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row n=0 : 1, 0, -1, -3, -2, -7, -5, -8, -3, -13, -10, -17, -7, -18, -11, ...
row n=1 : 1, 1, 0, -1, -1, -4, -3, -5, -2, -9, -7, -12, -5, -13, ...
row n=2 : 1, 2, 1, 1, 0, -1, -1, -2, -1, -5, -4, -7, -3, ...
row n=3 : 1, 3, 2, 3, 1, 2, 1, 1, 0, -1, -1, -2, -1, ...
row n=4 : 1, 4, 3, 5, 2, 5, 3, 4, 1, 3, 2, 3, 1, ...
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CROSSREFS
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Cf. A049456 A070878 A070879 A049455 A002487.
Adjacent sequences: A089592 A089593 A089594 this_sequence A089596 A089597 A089598
Sequence in context: A052311 A100950 A021335 this_sequence A034389 A084196 A127913
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KEYWORD
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sign,tabl
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AUTHOR
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DELEHAM Philippe ( kolotoko(AT)wanadoo.fr), Dec 30 2003
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