A317892 Number of nX4 0..1 arrays with every element unequal to 2, 3 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 2, 13, 82, 549, 3697, 25169, 170608, 1156219, 7839519, 53154565, 360388169, 2443433405, 16566593998, 112322259076, 761549454562, 5163336422278, 35007634908875, 237353212759913, 1609264585122172, 10910880368099881

Offset

1,2

Comments

Column 4 of A317896.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 10*a(n-1) -31*a(n-2) +92*a(n-3) -221*a(n-4) +144*a(n-5) -125*a(n-6) -169*a(n-7) +1231*a(n-8) +2495*a(n-9) -3384*a(n-10) +5083*a(n-11) -5257*a(n-12) -28179*a(n-13) -6771*a(n-14) +3549*a(n-15) -14557*a(n-16) +77495*a(n-17) +143971*a(n-18) +91139*a(n-19) +96950*a(n-20) -44694*a(n-21) -239000*a(n-22) -395274*a(n-23) -505737*a(n-24) -331428*a(n-25) -184844*a(n-26) +98400*a(n-27) +220028*a(n-28) +618689*a(n-29) +734341*a(n-30) +885867*a(n-31) +765523*a(n-32) +563084*a(n-33) +149323*a(n-34) -95273*a(n-35) -323108*a(n-36) -344668*a(n-37) -268599*a(n-38) -148723*a(n-39) -57429*a(n-40) +36378*a(n-41) +53163*a(n-42) +30807*a(n-43) +14338*a(n-44) +6375*a(n-45) -2291*a(n-46) -2889*a(n-47) -702*a(n-48) -238*a(n-49) -97*a(n-50) +2*a(n-51) +19*a(n-52) -4*a(n-54) for n>56

Example

Some solutions for n=5
..0..1..0..0. .0..1..0..0. .0..1..0..0. .0..1..0..1. .0..1..0..0
..1..0..1..1. .1..0..1..1. .1..1..1..1. .1..0..1..0. .1..1..1..1
..0..1..1..0. .0..1..1..0. .0..0..0..0. .1..0..1..1. .0..0..0..0
..0..1..0..1. .0..0..0..1. .1..0..0..1. .0..0..1..0. .1..1..1..1
..1..0..1..0. .1..1..1..0. .1..0..1..0. .1..1..0..1. .0..0..1..0

Crossrefs

Cf. A317896.

Sequence in context: A074581 A020059 A162772 * A079752 A156018 A285795

Adjacent sequences: A317889 A317890 A317891 * A317893 A317894 A317895

Keyword

nonn

Author

R. H. Hardin, Aug 10 2018

Status

approved