A389504 a(n) = Sum_{i=1..n} (Product_{j=1..n} M(j, ((i+j-2) mod n)+1) + Product_{j=1..n} M(j, ((i-j-1) mod n)+1)) where M is an n X n Toeplitz matrix whose first row consists of successive positive integer numbers 1, ..., n and whose first column consists of 1, n + 1, ..., 2*n - 1.

0, 2, 14, 100, 1297, 16058, 308703, 5896708, 148130421, 3860558314, 119255469971, 3901287045364, 143146822914905, 5591575671662650, 237947065419560087, 10761402142918494788, 521554787785961031773, 26753381390688751087914, 1455599338968114100228795, 83434758863105950027383412

Offset

0,2

Comments

It differs from A389503 in the sign between the two products.

Links

Table of n, a(n) for n=0..19.

Example

a(3) = A322909(3) = 100:
  [1, 2, 3]
  [4, 1, 2]
  [5, 4, 1]

Mathematica

p[i_]:=i; M[i_, j_, n_]:=Part[Part[ToeplitzMatrix[Join[{p[1]}, Array[p, n-1, {n+1, 2*n-1}]], Array[p, n]], i], j]; a[n_]:=Sum[Product[M[j, Mod[i+j-2, n]+1, n], {j, n}]+Product[M[j, Mod[i-j-1, n]+1, n], {j, n}], {i, n}]; Array[a, 20, 0]

Crossrefs

Cf. A322909, A389276, A389503.

Sequence in context: A074620 A185010 A144277 * A037726 A037621 A085372

Adjacent sequences: A389501 A389502 A389503 * A389505 A389506 A389507

Keyword

nonn

Author

Stefano Spezia, Oct 07 2025

Status

approved