The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A345908

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A345908

Traces of the matrices (A345197) counting integer compositions by length and alternating sum.
(history; published version)

#14 by Peter Luschny at Thu Aug 04 05:07:42 EDT 2022

STATUS

reviewed

approved

#13 by Michel Marcus at Thu Aug 04 02:13:57 EDT 2022

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proposed

reviewed

#12 by Jon E. Schoenfield at Thu Aug 04 00:03:49 EDT 2022

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editing

proposed

#11 by Jon E. Schoenfield at Thu Aug 04 00:03:46 EDT 2022

CROSSREFS

Diagonals and anti-diagonals antidiagonals of the same matrices are A346632 and A345907.

STATUS

approved

editing

#10 by Alois P. Heinz at Wed Aug 11 05:49:30 EDT 2021

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proposed

approved

#9 by Jon E. Schoenfield at Wed Aug 11 05:46:33 EDT 2021

STATUS

editing

proposed

#8 by Jon E. Schoenfield at Wed Aug 11 05:46:31 EDT 2021

COMMENTS

The matrices (A345197) count the number of integer compositions of n of length k with alternating sum i, where 1 <= k <= n, and i ranges from -n + 2 to n in steps of 2. Here, the alternating sum of a sequence (y_1,...,y_k) is Sum_i (-1)^(i-1) y_i. So a(n) is the number of compositions of n of length (n + s)/2, where s is the alternating sum of the composition.

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approved

editing

#7 by Susanna Cuyler at Tue Jul 27 21:18:14 EDT 2021

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proposed

approved

#6 by Gus Wiseman at Tue Jul 27 19:52:47 EDT 2021

STATUS

editing

proposed

#5 by Gus Wiseman at Tue Jul 27 15:26:32 EDT 2021

CROSSREFS

Cf. A000070, A000346, A001405, A007318, A008549, A025047, A114121, A163493, A344610.