A183655 Number of (n+1) X 3 0..5 arrays with every 2 X 2 subblock summing to 10.

666, 2442, 9990, 43986, 204246, 987762, 4934070, 25308786, 132730326, 709335282, 3852616950, 21219113586, 118292970006, 666434422002, 3788953272630, 21712782262386, 125279753843286, 727120126151922, 4241619956725110, 24850938484419186, 146138489780630166, 862101916492749042

Offset

1,1

Links

Zhuorui He, Table of n, a(n) for n = 1..1000 (first 200 terms from R. H. Hardin)

Christian Krause, Proof of formulas, Jun 12 2026.

Index entries for linear recurrences with constant coefficients, signature (21,-175,735,-1624,1764,-720).

Formula

a(n) = 21*a(n-1) - 175*a(n-2) + 735*a(n-3) - 1624*a(n-4) + 1764*a(n-5) - 720*a(n-6).

G.f.: 6*x*(111 - 1924*x + 12543*x^2 - 37994*x^3 + 52584*x^4 - 25920*x^5) / ((1 - x)*(1 - 2*x)*(1 - 3*x)*(1 - 4*x)*(1 - 5*x)*(1 - 6*x)). - Colin Barker, Apr 02 2018

a(n) = 6*6^n + 30*5^n + 48*4^n + 54*3^n + 48*2^n + 30. - Christian Krause, Jun 12 2026

E.g.f.: 6*(exp(6*x) + 5*exp(5*x) + 8*exp(4*x) + 9*exp(3*x) + 8*exp(2*x) + 5*exp(x) - 36). - Stefano Spezia, Jun 20 2026

Example

Some solutions for 5 X 3:
..5..0..5....2..1..1....1..4..1....1..5..1....4..1..1....2..3..5....3..0..3
..5..0..5....3..4..4....0..5..0....3..1..3....2..3..5....4..1..1....5..2..5
..1..4..1....3..0..2....2..3..2....5..1..5....5..0..2....2..3..5....1..2..1
..1..4..1....4..3..5....2..3..2....0..4..0....1..4..4....5..0..2....4..3..4
..2..3..2....3..0..2....1..4..1....2..4..2....3..2..0....0..5..3....2..1..2

Mathematica

A183655[n_] := 6*6^n + 30*5^n + 48*4^n + 54*3^n + 48*2^n + 30;
Array[A183655, 25] (* Paolo Xausa, Jun 17 2026 *)

Crossrefs

Column 2 of A183662.

Cf. A183653-A183661.

Sequence in context: A062045 A043515 A051003 * A104181 A221014 A057564

Adjacent sequences: A183652 A183653 A183654 * A183656 A183657 A183658

Keyword

nonn,easy,changed

Author

R. H. Hardin, Jan 06 2011

Status

approved