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

1,1

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

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).

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 *)

Crossrefs

Sequence in context: A302413 A303180 A188820 * A231299 A029534 A120046

Adjacent sequences: A181206 A181207 A181208 * A181210 A181211 A181212

Keyword

nonn

Author

R. H. Hardin, Oct 10 2010

Status

approved