A207809 Number of 4 X n 0..1 arrays avoiding 0 0 0 and 0 0 1 horizontally and 0 1 0 and 1 0 1 vertically.

10, 100, 370, 1970, 9040, 43990, 209050, 1002960, 4793390, 22944590, 109759520, 525189790, 2512723030, 12022412680, 57521607650, 275215898890, 1316784620900, 6300231318630, 30143802148430, 144224703156300, 690051081572450

Offset

1,1

Comments

Row 4 of A207808.

Links

Robert Israel and R. H. Hardin, Table of n, a(n) for n = 1..1460 (n = 1..210 from R. H. Hardin)

Robert Israel, Maple code to verify recursion

Index entries for linear recurrences with constant coefficients, signature (2,13,4,-12,1,1).

Formula

Empirical: a(n) = 2*a(n-1) +13*a(n-2) +4*a(n-3) -12*a(n-4) +a(n-5) +a(n-6)

From Robert Israel, Jul 03 2016: (Start)

The empirical recursion is true: see link for Maple verification.

G.f.: (10*x+80*x^2+40*x^3-110*x^4+10*x^5+10*x^6)/(1-2*x-13*x^2-4*x^3+12*x^4-x^5-x^6). (End)

Example

Some solutions for n=4:
..0..1..1..0....0..1..0..1....0..1..1..0....0..1..1..0....1..0..1..1
..1..1..0..0....1..0..1..1....0..1..1..1....0..1..0..1....0..1..0..0
..1..1..0..0....1..0..1..0....1..1..0..1....0..1..0..1....0..1..0..0
..0..1..1..1....1..1..0..0....1..1..0..1....1..1..0..1....1..0..1..0

Maple

f:= gfun:-rectoproc({a(n)=2*a(n-1) +13*a(n-2) +4*a(n-3) -12*a(n-4) +a(n-5) +a(n-6), seq(a(i)=[10, 100, 370, 1970, 9040, 43990][i], i=1..6)}, a(n), remember):
map(f, [$1..50]); # Robert Israel, Jul 03 2016

Crossrefs

Cf. A207808.

Sequence in context: A207255 A207950 A207859 * A208283 A208416 A208024

Adjacent sequences: A207806 A207807 A207808 * A207810 A207811 A207812

Keyword

nonn

Author

R. H. Hardin, Feb 20 2012

Status

approved