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A262759 T(n,k) = Number of (n+2) X (k+2) 0..1 arrays with each row divisible by 5 and each column divisible by 7, read as a binary number with top and left being the most significant bits. 13

%I #6 Aug 19 2022 15:03:07

%S 2,4,3,7,9,5,13,17,25,10,26,37,49,100,19,52,107,129,319,361,37,103,

%T 321,709,1645,1345,1369,74,205,865,4953,16450,8605,6193,5476,147,410,

%U 2449,16705,243220,135595,52993,39751,21609,293,820,7299,73345,1614175

%N T(n,k) = Number of (n+2) X (k+2) 0..1 arrays with each row divisible by 5 and each column divisible by 7, read as a binary number with top and left being the most significant bits.

%C Table starts

%C ...2......4.......7.......13........26.........52........103.........205

%C ...3......9......17.......37.......107........321........865........2449

%C ...5.....25......49......129.......709.......4953......16705.......73345

%C ..10....100.....319.....1645.....16450.....243220....1614175....15350125

%C ..19....361....1345.....8605....135595....3051121...31840777...475175089

%C ..37...1369....6193....52993...1635877...71515801.1252506169.32264365249

%C ..74...5476...39751...658381..37426418.3270912532

%C .147..21609..229841..5747701.595006235

%C .293..85849.1339569.51979793

%C .586.343396.8663743

%H R. H. Hardin, <a href="/A262759/b262759.txt">Table of n, a(n) for n = 1..84</a>

%F Empirical for column k:

%F k=1: a(n) = 2*a(n-1) +a(n-3) -2*a(n-4)

%F k=2: a(n) = 4*a(n-1) +9*a(n-3) -36*a(n-4) -8*a(n-6) +32*a(n-7)

%F Empirical for row n:

%F n=1: a(n) = 3*a(n-1) -3*a(n-2) +3*a(n-3) -2*a(n-4)

%F n=2: [order 8]

%F n=3: [order 17]

%F n=4: [order 16]

%e Some solutions for n=4, k=4

%e ..1..0..0..0..1..1....1..1..1..1..0..0....1..0..0..0..1..1....1..1..1..1..0..0

%e ..1..0..1..0..0..0....1..1..1..1..0..0....1..0..1..1..0..1....1..1..0..0..1..0

%e ..1..0..0..0..1..1....1..1..1..1..0..0....1..0..1..0..0..0....1..0..1..1..0..1

%e ..1..1..1..1..0..0....0..1..1..0..0..1....1..1..1..1..0..0....1..0..0..0..1..1

%e ..1..1..0..1..1..1....0..1..1..0..0..1....1..1..0..0..1..0....1..0..1..1..0..1

%e ..1..1..1..1..0..0....0..1..1..0..0..1....1..1..0..1..1..1....1..1..0..0..1..0

%Y Column 1 is A046630.

%Y Row 1 is A262267.

%Y Row 2 is A262466(n+1).

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Sep 30 2015

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)