A295547 Number of nX4 0..1 arrays with each 1 horizontally or vertically adjacent to 1, 3 or 4 1s.

4, 24, 116, 598, 3035, 15352, 78434, 399324, 2032606, 10348672, 52692507, 268312054, 1366173209, 6956133881, 35419004021, 180345636773, 918277914237, 4675652060491, 23807313576093, 121221249954751, 617230101640978

Offset

1,1

Comments

Column 4 of A295551.

Links

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

Robert Israel, Maple-assisted proof of formula

Formula

Empirical: a(n) = 7*a(n-1) -8*a(n-2) -7*a(n-3) +10*a(n-4) -84*a(n-5) -232*a(n-6) +680*a(n-7) +1299*a(n-8) -1669*a(n-9) -475*a(n-10) +3475*a(n-11) -5871*a(n-12) -8620*a(n-13) +4957*a(n-14) -3601*a(n-15) -7232*a(n-16) +1897*a(n-17) +10512*a(n-18) +544*a(n-19) +795*a(n-20) +21086*a(n-21) +6396*a(n-22) +19576*a(n-23) +6829*a(n-24) +16929*a(n-25) -15374*a(n-26) +664*a(n-27) -12805*a(n-28) -19325*a(n-29) -17150*a(n-30) -12843*a(n-31) -15082*a(n-32) -5335*a(n-33) -8181*a(n-34) -58*a(n-35) -3152*a(n-36) +1066*a(n-37) -493*a(n-38) +294*a(n-39) +37*a(n-40) +15*a(n-41) +24*a(n-42) +12*a(n-43) -a(n-44) -a(n-45).

Empirical formula confirmed (see link). - Robert Israel, Nov 23 2017

Example

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

Crossrefs

Cf. A295551.

Sequence in context: A295093 A211142 A272735 * A270451 A037132 A067312

Adjacent sequences: A295544 A295545 A295546 * A295548 A295549 A295550

Keyword

nonn

Author

R. H. Hardin, Nov 23 2017

Status

approved