OFFSET
1,1
COMMENTS
Column 2 of A231586
LINKS
Robert Israel, Table of n, a(n) for n = 1..1488 (first 210 terms from R. H. Hardin)
Robert Israel, Maple-assisted proof of formula
FORMULA
Empirical: a(n) = 4*a(n-1) +6*a(n-2) +38*a(n-3) -161*a(n-4) -292*a(n-5) -953*a(n-6) +1185*a(n-7) +4928*a(n-8) +12336*a(n-9) +7076*a(n-10) -7076*a(n-11) -24464*a(n-12) -24608*a(n-13) -18624*a(n-14) -6720*a(n-15) -2304*a(n-16).
Empirical formula verified by Robert Israel, Dec 06 2017 (see link).
EXAMPLE
Some solutions for n=7
..0..0....3..0....2..1....0..3....2..0....2..3....2..2....1..1....3..3....0..0
..0..2....0..0....1..1....0..0....0..0....2..2....0..0....2..1....0..0....0..1
..1..0....0..0....0..0....0..1....1..0....3..2....0..0....1..2....0..0....0..0
..0..0....0..2....0..0....0..2....0..0....1..1....1..3....0..0....0..3....3..0
..2..0....0..1....0..2....0..0....0..1....1..1....0..0....0..0....0..0....0..1
..2..0....0..0....2..0....0..0....0..0....1..1....0..0....0..0....3..0....0..0
..0..0....0..0....0..0....2..0....3..0....2..1....2..3....0..2....0..0....0..3
MAPLE
rec:= a(n) = 4*a(n-1) +6*a(n-2) +38*a(n-3) -161*a(n-4) -292*a(n-5) -953*a(n-6) +1185*a(n-7) +4928*a(n-8) +12336*a(n-9) +7076*a(n-10) -7076*a(n-11) -24464*a(n-12) -24608*a(n-13) -18624*a(n-14) -6720*a(n-15) -2304*a(n-16):
Data := [4, 28, 124, 602, 2776, 12922, 60720, 286047, 1335296, 6256326, 29377828, 137595239, 644951590, 3024402309, 14175895645, 66459189937]:
f:= gfun:-rectoproc({rec, seq(a(i)=Data[i], i=1..16)}, a(n), remember):
map(f, [$1..40]); # Robert Israel, Dec 06 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
R. H. Hardin, Nov 11 2013
STATUS
approved