A300310 Number of nX4 0..1 arrays with every element equal to 0, 1, 2, 4, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

8, 29, 45, 211, 1537, 8135, 41485, 237494, 1335377, 7220188, 39898274, 222289040, 1223973190, 6747658497, 37357592557, 206400784559, 1139340023954, 6296448768518, 34794231928876, 192191214782093, 1061796400589644

Offset

1,1

Comments

Column 4 of A300314.

Links

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

Formula

Empirical: a(n) = 8*a(n-1) -18*a(n-2) +70*a(n-3) -322*a(n-4) +361*a(n-5) -313*a(n-6) +3440*a(n-7) -10094*a(n-8) +16988*a(n-9) -28221*a(n-10) +73982*a(n-11) -199678*a(n-12) +479468*a(n-13) -793158*a(n-14) +925262*a(n-15) -1954164*a(n-16) +4127614*a(n-17) -6407292*a(n-18) +8175969*a(n-19) -8673631*a(n-20) +12171733*a(n-21) -16358559*a(n-22) +19137438*a(n-23) -16516504*a(n-24) +10215879*a(n-25) -19973774*a(n-26) +20952359*a(n-27) -11874866*a(n-28) +6728183*a(n-29) -5330656*a(n-30) +8897807*a(n-31) -7767199*a(n-32) -2301042*a(n-33) +21535378*a(n-34) -18718181*a(n-35) +19792800*a(n-36) -24230147*a(n-37) +24223480*a(n-38) -20874941*a(n-39) +6026189*a(n-40) -619358*a(n-41) -5800306*a(n-42) +3505724*a(n-43) +471730*a(n-44) +1046928*a(n-45) +577343*a(n-46) +176833*a(n-47) -194370*a(n-48) -207100*a(n-49) -27997*a(n-50) -10625*a(n-51) +7207*a(n-52) +5466*a(n-53) +194*a(n-54) +204*a(n-55) for n>59

Example

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

Crossrefs

Cf. A300314.

Sequence in context: A299011 A299802 A299678 * A171442 A341402 A247541

Adjacent sequences: A300307 A300308 A300309 * A300311 A300312 A300313

Keyword

nonn

Author

R. H. Hardin, Mar 02 2018

Status

approved