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A181209 Number of n X 5 binary matrices with no two 1's adjacent diagonally or antidiagonally.

%I A181209 #18 Aug 30 2024 12:27:35
%S A181209 32,169,2117,17424,177073,1630729,15786848,149352841,1429585373,
%T A181209 13610488896,129934154497,1238878076401,11819811992192,
%U A181209 112736763711049,1075437390934037,10258292274099984,97854335246290033,933422273708422969
%N A181209 Number of n X 5 binary matrices with no two 1's adjacent diagonally or antidiagonally.
%C A181209 Column 5 of A181212.
%H A181209 Robert Israel, <a href="/A181209/b181209.txt">Table of n, a(n) for n = 1..1019</a> (n = 1..250 from R. H. Hardin)
%H A181209 Robert Israel, <a href="/A181209/a181209.pdf">Maple-assisted proof of formula</a>
%H A181209 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (12, 0, -283, 516, 600, -1415, 0, 600, -125).
%F A181209 Empirical: a(n) = 12*a(n-1) - 283*a(n-3) + 516*a(n-4) + 600*a(n-5) - 1415*a(n-6) + 600*a(n-8) - 125*a(n-9).
%F A181209 Formula verified by _Robert Israel_, Dec 25 2017 (see link).
%p A181209 f:= gfun:-rectoproc({a(n)=12*a(n-1)-283*a(n-3)+516*a(n-4)+600*a(n-5)-1415*a(n-6)+600*a(n-8)-125*a(n-9),a(1) = 32, a(2) = 169, a(3) = 2117, a(4) = 17424, a(5) = 177073, a(6) = 1630729, a(7) = 15786848, a(8) = 149352841,a(9)=1429585373},a(n),remember):
%p A181209 map(f, [$1..30]); # _Robert Israel_, Dec 25 2017
%t A181209 RecurrenceTable[{a[n] == 12*a[n - 1] - 283*a[n - 3] + 516*a[n - 4] + 600*a[n - 5] - 1415*a[n - 6] + 600*a[n - 8] - 125*a[n - 9], a[1] == 32, a[2] == 169, a[3] == 2117, a[4] == 17424, a[5] == 177073, a[6] == 1630729, a[7] == 15786848, a[8] == 149352841, a[9] == 1429585373}, a, {n, 1, 30}] (* _Jean-François Alcover_, Aug 29 2022, after _Robert Israel_ *)
%K A181209 nonn
%O A181209 1,1
%A A181209 _R. H. Hardin_, Oct 10 2010