The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A353453 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A353453

a(n) is the permanent of the n X n symmetric matrix M(n) that is defined as M[i,j] = abs(i - j) if min(i, j) < max(i, j) <= 2*min(i, j), and otherwise 0.
(history; published version)

#18 by Alois P. Heinz at Tue Aug 29 20:18:26 EDT 2023

STATUS

proposed

approved

#17 by Chai Wah Wu at Tue Aug 29 17:18:11 EDT 2023

STATUS

editing

proposed

#16 by Chai Wah Wu at Tue Aug 29 17:18:08 EDT 2023

PROG

(Python)

from sympy import Matrix

def A353453(n): return Matrix(n, n, lambda i, j: abs(i-j) if min(i, j)<max(i, j)<=(min(i, j)<<1)+1 else 0).per() if n else 1 # Chai Wah Wu, Aug 29 2023

STATUS

approved

editing

#15 by Michael De Vlieger at Thu Apr 28 07:48:52 EDT 2022

STATUS

reviewed

approved

#14 by Michel Marcus at Thu Apr 28 02:22:45 EDT 2022

STATUS

proposed

reviewed

#13 by Stefano Spezia at Mon Apr 25 06:38:06 EDT 2022

STATUS

editing

proposed

#12 by Stefano Spezia at Mon Apr 25 06:25:53 EDT 2022

FORMULA

Sum_{i=1..n} Sum_{j=1..n} M[i,j]^2 = A350050(n+1).

CROSSREFS

Cf. A000982 (number of zero matrix elements), A003983, A006918, A007590 (number of positive matrix elements), A049581, A051125, A173997, A350050, A352967, A353452 (determinant).

STATUS

proposed

editing

#11 by Stefano Spezia at Sun Apr 24 08:05:33 EDT 2022

STATUS

editing

proposed

#10 by Stefano Spezia at Sun Apr 24 08:04:46 EDT 2022

CROSSREFS

Cf. A000982 (number of zero matrix elements), A003983, A006918, A007590 (number of positive matrix elements), A049581, A051125, A173997, A352867, A352967, A353452 (determinant).

#9 by Stefano Spezia at Sun Apr 24 08:04:28 EDT 2022

CROSSREFS

Cf. A000982 (number of zero matrix elements), A003983, A006918, A007590 (number of positive matrix elements), A049581, A051125, A173997, A352867, A353452 (determinant).

STATUS

proposed

editing