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

32, 169, 2117, 17424, 177073, 1630729, 15786848, 149352841, 1429585373, 13610488896, 129934154497, 1238878076401, 11819811992192, 112736763711049, 1075437390934037, 10258292274099984, 97854335246290033, 933422273708422969

Offset: 1

Author

R. H. Hardin, Oct 10 2010

Keywords

• nonn

Comments

Column 5 of A181212.

Links

• Robert Israel, Table of n, a(n) for n = 1..1019 (n = 1..250 from R. H. Hardin)
• Robert Israel, Maple-assisted proof of formula
• Index entries for linear recurrences with constant coefficients, signature (12, 0, -283, 516, 600, -1415, 0, 600, -125).

Programs

Maple

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):
map(f, [$1..30]); # Robert Israel, Dec 25 2017

Mathematica

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 *)

Formula

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).

Formula verified by Robert Israel, Dec 25 2017 (see link).