# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a353453 Showing 1-1 of 1 %I A353453 #18 Aug 29 2023 20:18:26 %S A353453 1,0,1,0,1,4,64,576,7844,63524,882772,11713408,252996564,5879980400, %T A353453 184839020672,5698866739200,229815005974352,9350598794677712, %U A353453 480306381374466176,23741710999960266176,1446802666239931811472,86153125248221968292928,6197781268948296566634304 %N 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. %F A353453 Sum_{i=1..n+1-k} M[i,i+k] = A173997(n, k) with 1 <= k <= floor((n + 1)/2). %F A353453 Sum_{i=1..n} Sum_{j=1..n} M[i,j] = 2*A006918(n-1). %F A353453 Sum_{i=1..n} Sum_{j=1..n} M[i,j]^2 = A350050(n+1). %e A353453 a(8) = 7844: %e A353453 0, 1, 0, 0, 0, 0, 0, 0; %e A353453 1, 0, 1, 2, 0, 0, 0, 0; %e A353453 0, 1, 0, 1, 2, 3, 0, 0; %e A353453 0, 2, 1, 0, 1, 2, 3, 4; %e A353453 0, 0, 2, 1, 0, 1, 2, 3; %e A353453 0, 0, 3, 2, 1, 0, 1, 2; %e A353453 0, 0, 0, 3, 2, 1, 0, 1; %e A353453 0, 0, 0, 4, 3, 2, 1, 0. %t A353453 Join[{1},Table[Permanent[Table[If[Min[i,j]