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A196574 Number of n X 4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 1,2,3,0,4 for x=0,1,2,3,4. 1
1, 7, 37, 145, 971, 4787, 24837, 134167, 700787, 3689127, 19500651, 102652203, 541025795, 2852510953, 15032123527, 79230081799, 417611039473, 2201042540865, 11601003412043, 61145318600329, 322275993958125, 1698611779257449 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Every 0 is next to 0 1's, every 1 is next to 1 2's, every 2 is next to 2 3's, every 3 is next to 3 0's, every 4 is next to 4 4's.

Column 4 of A196578.

LINKS

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

FORMULA

Empirical: a(n) = 2*a(n-1) +9*a(n-2) +39*a(n-3) +20*a(n-4) +12*a(n-5) +32*a(n-6) -17*a(n-7) +a(n-8) -4*a(n-9) +a(n-10).

Empirical g.f.: x*(1 + 5*x + 14*x^2 - 31*x^3 + 55*x^4 - 55*x^5 + 13*x^6 - 10*x^7 + x^8 + x^9) / (1 - 2*x - 9*x^2 - 39*x^3 - 20*x^4 - 12*x^5 - 32*x^6 + 17*x^7 - x^8 + 4*x^9 - x^10). - Colin Barker, May 09 2018

EXAMPLE

Some solutions for n=5:

..0..0..0..0....0..0..3..0....0..3..0..0....0..0..0..0....0..0..3..0

..0..3..0..0....3..0..0..3....0..0..0..0....0..0..0..3....0..0..0..0

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

..0..0..0..0....0..0..0..3....3..0..0..0....0..0..3..0....0..0..0..0

..0..3..0..0....0..0..0..0....0..3..0..0....0..3..0..0....0..0..0..0

CROSSREFS

Cf. A196578.

Sequence in context: A243893 A012885 A162541 * A094729 A202659 A202119

Adjacent sequences: A196571 A196572 A196573 * A196575 A196576 A196577

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 04 2011

STATUS

approved

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Last modified December 2 14:15 EST 2022. Contains 358510 sequences. (Running on oeis4.)