login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A198405 Number of 2n X 2 0..4 arrays with values 0..4 introduced in row major order and each element equal to exactly one horizontal and vertical neighbor. 2
2, 17, 377, 11473, 375273, 12456897, 414711897, 13814539697, 460231956937, 15333001667233, 510833776539193, 17018936996199057, 567002973887727017, 18890274083549781377, 629348476275500726297, 20967377362990867086193 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 1 of A198408.

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..200

FORMULA

Empirical: a(n) = 51*a(n-1) - 691*a(n-2) + 3601*a(n-3) - 7056*a(n-4) + 4096*a(n-5).

Conjectures from Colin Barker, Mar 02 2018: (Start)

G.f.: x*(2 - 85*x + 892*x^2 - 3209*x^3 + 3552*x^4) / ((1 - x)*(1 - 9*x + 16*x^2)*(1 - 41*x + 256*x^2)).

a(n) = (2^(-8-n)*(-1752*(9-sqrt(17))^n*(-51+5*sqrt(17)) + 1752*(9+sqrt(17))^n*(51+5*sqrt(17)) + 17*(73*2^(9+n) + (365-17*sqrt(73))*(41-3*sqrt(73))^n + (41+3*sqrt(73))^n*(365+17*sqrt(73))))) / 3723.

(End)

EXAMPLE

Some solutions for n=3:

..0..0....0..0....0..1....0..0....0..0....0..0....0..0....0..1....0..0....0..1

..1..2....1..2....0..1....1..1....1..1....1..2....1..1....0..1....1..1....0..1

..1..2....1..2....2..3....2..3....2..3....1..2....2..2....2..2....0..0....2..3

..3..3....0..0....2..3....2..3....2..3....2..0....3..3....0..0....2..2....2..3

..4..0....3..2....1..0....3..0....4..4....2..0....4..4....1..3....0..0....4..4

..4..0....3..2....1..0....3..0....2..2....1..1....2..2....1..3....1..1....3..3

CROSSREFS

Cf. A198408.

Sequence in context: A243509 A128159 A319591 * A202972 A085617 A152557

Adjacent sequences:  A198402 A198403 A198404 * A198406 A198407 A198408

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 24 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 22 11:17 EDT 2021. Contains 345375 sequences. (Running on oeis4.)