A353452 - OEIS

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A353452

a(n) is the determinant 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.

1, 0, -1, 0, 1, -4, 12, 64, -172, -1348, 3456, 34240, -87084, 370640, -872336, -22639616, 52307088, -181323568, 399580288, 23627011200, -51305628400, -686160247552, 1545932859328, 68098264912128, -155370174372864, 6326621032802304, -13829529077133312, -1087288396552040448

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,6

LINKS

Table of n, a(n) for n=0..27.

FORMULA

Sum_{i=1..n+1-k} M[i,i+k] = A173997(n, k) with 1 <= k <= floor((n + 1)/2).

Sum_{i=1..n} Sum_{j=1..n} M[i,j] = 2*A006918(n-1).

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

EXAMPLE

a(8) = -172:

0, 1, 0, 0, 0, 0, 0, 0;

1, 0, 1, 2, 0, 0, 0, 0;

0, 1, 0, 1, 2, 3, 0, 0;

0, 2, 1, 0, 1, 2, 3, 4;

0, 0, 2, 1, 0, 1, 2, 3;

0, 0, 3, 2, 1, 0, 1, 2;

0, 0, 0, 3, 2, 1, 0, 1;

0, 0, 0, 4, 3, 2, 1, 0.

MATHEMATICA

Join[{1}, Table[Det[Table[If[Min[i, j]<Max[i, j]<=2Min[i, j], Abs[j-i], 0], {i, n}, {j, n}]], {n, 27}]]

PROG

(PARI) a(n) = matdet(matrix(n, n, i, j, if ((min(i, j) < max(i, j)) && (max(i, j) <= 2*min(i, j)), abs(i-j)))); \\ Michel Marcus, Apr 20 2022

(Python)

from sympy import Matrix

def A353452(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).det() # Chai Wah Wu, Aug 29 2023

CROSSREFS

Cf. A085750, A085807.

Cf. A000982 (number of zero matrix elements), A003983, A006918, A007590 (number of positive matrix elements), A049581, A051125, A173997, A350050, A352967, A353453 (permanent).

Sequence in context: A291772 A222645 A259816 * A071769 A221667 A275527

Adjacent sequences: A353449 A353450 A353451 * A353453 A353454 A353455

KEYWORD

sign

AUTHOR

Stefano Spezia, Apr 19 2022

STATUS

approved