A202119 - OEIS

%I #10 Sep 22 2019 13:39:18

%S 7,37,153,475,1509,4763,15101,47889,151833,481519,1527001,4842421,

%T 15356565,48699233,154436377,489754155,1553125143,4925322519,

%U 15619350977,49532617623,157079520865,498135926335,1579705609759,5009616203811

%N Number of -3..3 arrays of n elements with first, second and third differences also in -3..3.

%H R. H. Hardin, <a href="/A202119/b202119.txt">Table of n, a(n) for n = 1..210</a>

%H Robert Israel, <a href="/A202119/a202119.pdf">Maple-assisted proof of empirical formula</a>

%F Empirical: a(n) = 4*a(n-1) -5*a(n-2) +13*a(n-3) -19*a(n-4) +14*a(n-5) -32*a(n-6) +8*a(n-7) +4*a(n-8) +24*a(n-9) +27*a(n-10) +26*a(n-11) -48*a(n-12) -29*a(n-13) -56*a(n-14) -55*a(n-15) +134*a(n-16) -80*a(n-17) +244*a(n-18) -170*a(n-19) +149*a(n-20) -175*a(n-21) +70*a(n-22) -68*a(n-23) +32*a(n-24) -22*a(n-25) +2*a(n-26) -8*a(n-27) +a(n-28) +2*a(n-29) +2*a(n-30) for n>35.

%F Empirical formula verified: see link. - _Robert Israel_, Sep 22 2019

%e Some solutions for n=7

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

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

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

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

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

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

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

%Y Column 3 of A202124.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 11 2011