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A181256 Number of (n+2)X4 binary matrices with every 3X3 block having exactly four 1's 1
336, 746, 1684, 3942, 10348, 27554, 74784, 212570, 608476, 1755630, 5152996, 15171626, 44814936, 133231586, 396621844, 1182345462, 3533450908, 10565961074, 31613799504, 94685091050, 283660310476, 850017916350, 2548227410836 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Column 2 of A181262

LINKS

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

Robert Israel, Maple-assisted proof of formula

FORMULA

Empirical: a(n)=4*a(n-1)-3*a(n-2)+32*a(n-3)-128*a(n-4)+96*a(n-5)-375*a(n-6)+1500*a(n-7)-1125*a(n-8)+1980*a(n-9)-7920*a(n-10)+5940*a(n-11)-4644*a(n-12)+18576*a(n-13)-13932*a(n-14)+3888*a(n-15)-15552*a(n-16)+11664*a(n-17).

Empirical formula verified by Robert Israel, Jul 11 2018 (see link).

EXAMPLE

Some solutions for 5X4

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

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

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

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

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

MAPLE

okconfig:= proc(L) andmap(i -> L[i+1]+L[i+2]+L[i+3]+L[i+5]+L[i+6]+L[i+7]<=4, [$0..1]) end proc:

Configs:=  select(okconfig, [seq(convert(2^8+i, base, 2)[1..8], i=0..2^8-1)]):

Compatible:= proc(i, j) local k;

if Configs[i][1..4] <> Configs[j][5..8] then return 0 fi;

if add(Configs[i][k], k=[1, 2, 3, 5, 6, 7])+add(Configs[j][k], k=1..3)=4 and

    add(Configs[i][k], k=[2, 3, 4, 6, 7, 8])+add(Configs[j][k], k=2..4)=4 then 1 else 0 fi

end proc:

T:= Matrix(213, 213, Compatible):

v:= Vector(213, 1):

TV[0]:= v:

for n from 1 to 30 do TV[n]:= T . TV[n-1] od:

seq(v^%T . TV[n], n=1..30); # Robert Israel, Jul 11 2018

CROSSREFS

Sequence in context: A261551 A247530 A064259 * A006909 A067708 A059467

Adjacent sequences:  A181253 A181254 A181255 * A181257 A181258 A181259

KEYWORD

nonn

AUTHOR

R. H. Hardin, Oct 10 2010

STATUS

approved

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Last modified April 22 10:24 EDT 2019. Contains 322330 sequences. (Running on oeis4.)