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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.

%I A262759 #6 Aug 19 2022 15:03:07
%S A262759 2,4,3,7,9,5,13,17,25,10,26,37,49,100,19,52,107,129,319,361,37,103,
%T A262759 321,709,1645,1345,1369,74,205,865,4953,16450,8605,6193,5476,147,410,
%U A262759 2449,16705,243220,135595,52993,39751,21609,293,820,7299,73345,1614175
%N 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.
%C A262759 Table starts
%C A262759 ...2......4.......7.......13........26.........52........103.........205
%C A262759 ...3......9......17.......37.......107........321........865........2449
%C A262759 ...5.....25......49......129.......709.......4953......16705.......73345
%C A262759 ..10....100.....319.....1645.....16450.....243220....1614175....15350125
%C A262759 ..19....361....1345.....8605....135595....3051121...31840777...475175089
%C A262759 ..37...1369....6193....52993...1635877...71515801.1252506169.32264365249
%C A262759 ..74...5476...39751...658381..37426418.3270912532
%C A262759 .147..21609..229841..5747701.595006235
%C A262759 .293..85849.1339569.51979793
%C A262759 .586.343396.8663743
%H A262759 R. H. Hardin, <a href="/A262759/b262759.txt">Table of n, a(n) for n = 1..84</a>
%F A262759 Empirical for column k:
%F A262759 k=1: a(n) = 2*a(n-1) +a(n-3) -2*a(n-4)
%F A262759 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 A262759 Empirical for row n:
%F A262759 n=1: a(n) = 3*a(n-1) -3*a(n-2) +3*a(n-3) -2*a(n-4)
%F A262759 n=2: [order 8]
%F A262759 n=3: [order 17]
%F A262759 n=4: [order 16]
%e A262759 Some solutions for n=4, k=4
%e A262759 ..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 A262759 ..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 A262759 ..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 A262759 ..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 A262759 ..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 A262759 ..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 A262759 Column 1 is A046630.
%Y A262759 Row 1 is A262267.
%Y A262759 Row 2 is A262466(n+1).
%K A262759 nonn,tabl
%O A262759 1,1
%A A262759 _R. H. Hardin_, Sep 30 2015