A234191 - OEIS

%I #7 Mar 10 2022 20:45:06

%S 193264,10370036,552870656,29472668500,1570546543232,83690878669284,

%T 4459602725105968,237636889981332820,12662836664945997280,

%U 674758128948756836356,35955490268105707832016,1915941756734205665615988

%N Number of (n+2) X (1+2) 0..3 arrays with no increasing sequence of length 3 horizontally, diagonally downwards or antidiagonally downwards.

%C Column 1 of A234196.

%H R. H. Hardin, <a href="/A234191/b234191.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 56*a(n-1) -119*a(n-2) -1308*a(n-3) +23400*a(n-4) -1471264*a(n-5) +2773580*a(n-6) +41183056*a(n-7) -96018000*a(n-8) +164815744*a(n-9) -481311056*a(n-10) -1789740992*a(n-11) +2706969088*a(n-12) -1995040768*a(n-13) +114872384*a(n-14) +1679949056*a(n-15) -1477492736*a(n-16) +3012214784*a(n-17) -415727616*a(n-18) +599916544*a(n-19) -1973420032*a(n-20) +234881024*a(n-21) -167772160*a(n-22) +134217728*a(n-23).

%e Some solutions for n=1

%e ..1..3..0....1..0..3....0..3..3....2..0..1....1..3..1....1..0..3....1..2..0

%e ..2..2..2....3..3..1....3..1..3....1..3..2....0..3..2....3..1..3....3..3..1

%e ..2..2..1....1..1..0....2..2..0....1..1..1....1..0..0....3..1..2....2..1..2

%Y Cf. A234196.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 21 2013