A389428 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 the n X n matrix M(n) formed by writing the numbers 1, ..., n^2 successively forward and backward along the rows in zig-zag pattern.

0, 2, 22, 490, 19620, 1276314, 118208610, 15402929550, 2577841713288, 560839300633566, 148082321622642750, 48377789074407441474, 18507588952649475350700, 8469999266541156523993410, 4428981804705769644632786970, 2703448364063086192963721455350, 1851947838053160486721396338414096

Offset

0,2

Comments

It differs from A389427 in the sign between the two products.

Links

Table of n, a(n) for n=0..16.

Example

a(6) = 118208610:
  [ 1,  2,  3,  4,  5,  6]
  [12, 11, 10,  9,  8,  7]
  [13, 14, 15, 16, 17, 18]
  [24, 23, 22, 21, 20, 19]
  [25, 26, 27, 28, 29, 30]
  [36, 35, 34, 33, 32, 31]

Mathematica

M[i_, j_, n_] := 1 - j + i n + (-1 + 2 j - n) Mod[i, 2]; 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, 17, 0]

Crossrefs

Cf. A322277, A389276, A389427.

Sequence in context: A137076 A090730 A090313 * A110129 A328020 A246740

Adjacent sequences: A389425 A389426 A389427 * A389429 A389430 A389431

Keyword

nonn

Author

Stefano Spezia, Oct 03 2025

Status

approved