A390922 a(n) is the number of 2 X 2 matrices with elements 1..n where at least one row and at least one column is strictly increasing.

0, 0, 4, 29, 106, 280, 610, 1169, 2044, 3336, 5160, 7645, 10934, 15184, 20566, 27265, 35480, 45424, 57324, 71421, 87970, 107240, 129514, 155089, 184276, 217400, 254800, 296829, 343854, 396256, 454430, 518785, 589744, 667744, 753236, 846685, 948570, 1059384, 1179634, 1309841, 1450540, 1602280

Offset

0,3

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = (n - 1)*(7*n^3 - n^2 - 2*n)/12. - Jason Yuen, Dec 01 2025

Mathematica

a[n_, d_] := a[n, d] = (AnyTrue[#, OrderedQ[#, Less] &] && AnyTrue[Transpose[#], OrderedQ[#, Less] &] &) /@ Tuples[Range[1, n], {d, d}] // Boole // Total;
Table[a[n, 2], {n, 0, 42}]
A390922[n_] := n*(n - 1)*(n*(7*n - 1) - 2)/12;
Array[A390922, 50, 0] (* Paolo Xausa, Dec 09 2025 *)

Crossrefs

Cf. A390925 (3 X 3).

Cf. A206808 (2 X 2, row only), A390904 (3 X 3, row only).

Sequence in context: A199399 A211545 A295842 * A345897 A368372 A372424

Adjacent sequences: A390919 A390920 A390921 * A390923 A390924 A390925

Keyword

nonn,easy

Author

Robert P. P. McKone, Nov 24 2025

Status

approved