A183643 Number of (n+1) X (n+1) 0..4 arrays with every 2 X 2 subblock summing to 8.

85, 1001, 10213, 97145, 889525, 7969001, 70480453, 618704345, 5408906965, 47195168201, 411600373093, 3591377948345, 31370840111605, 274436978962601, 2404978079616133, 21114549286837145, 185724616500231445, 1636681979528120201, 14449071277812337573, 127778925903757978745

Offset

1,1

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

Christian Krause, Proof of formula, Jun 14 2026.

Index entries for linear recurrences with constant coefficients, signature (35,-497,3661,-14742,30744,-25920).

Formula

a(n) = 9*9^n + 16*8^n - 24*6^n + 10*5^n - 12*4^n + 6*3^n. - Christian Krause, Jun 14 2026

Example

Some solutions for 3X3
..3..2..1....2..1..0....1..3..0....2..0..4....2..1..2....3..2..2....3..2..3
..2..1..4....2..3..4....3..1..4....4..2..2....2..3..2....0..3..1....0..3..0
..2..3..0....2..1..0....1..3..0....1..1..3....2..1..2....1..4..0....2..3..2

Mathematica

A183643[n_] := 9*9^n + 16*8^n - 24*6^n + 10*5^n - 12*4^n + 6*3^n;
Array[A183643, 25] (* Paolo Xausa, Jun 15 2026 *)

Crossrefs

Diagonal of A183652.

Sequence in context: A202009 A194533 A069308 * A206163 A020239 A297587

Adjacent sequences: A183640 A183641 A183642 * A183644 A183645 A183646

Keyword

nonn,easy

Author

R. H. Hardin, Jan 06 2011

Extensions

a(7)-a(20) from Christian Krause, Jun 14 2026

Status

approved