OFFSET
1,1
COMMENTS
Table starts
....9...18....35....68...133...262...519..1032..2057..4106...8203..16396..32781
...18...34....62...114...214...410...798..1570..3110..6186..12334..24626..49206
...36...66...114...196...344...622..1158..2208..4284..8410..16634..33052..65856
...72..130...216...350...572...962..1680..3046..5700.10922..21272..41870..82956
..144..258...418...648...996..1558..2526..4284..7600.14010..26586..51472.100956
..288..514...820..1234..1812..2666..4020..6322.10468.18250..33252..62642.120756
..576.1026..1622..2396..3412..4798..6810..9960.15272.24794..42622..76948.144156
.1152.2050..3224..4710..6580..8978.12192.16798.23948.35946..57400..97526.174756
.2304.4098..6426..9328.12884.17254.22758.30036.40368.56314..82994.130648.219756
.4608.8194.12828.18554.25460.33722.43692.56074.72276.95114.130220.188858.293556
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..611
FORMULA
Empirical for column k: (k+2)^2*2^(n-1) plus a linear polynomial in n
k=1: a(n) = 2*a(n-1); a(n) = 9*2^(n-1)
k=2: a(n) = 3*a(n-1) -2*a(n-2); a(n) = 16*2^(n-1) + 2
k=3: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3); a(n) = 25*2^(n-1) + 2*n + 8
k=4: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3); a(n) = 36*2^(n-1) + 10*n + 22
k=5: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3); a(n) = 49*2^(n-1) + 32*n + 52
k=6: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3); a(n) = 64*2^(n-1) + 84*n + 114
k=7: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3); a(n) = 81*2^(n-1) + 198*n + 240
k=8: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3); a(n) = 100*2^(n-1) + 438*n + 494
k=9: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3); a(n) = 121*2^(n-1) + 932*n + 1004
Empirical for row n: (4*n+4)*2^(k-1) plus a quadratic polynomial in k
n=1: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3); a(n) = 8*2^(n-1) + n
n=2: a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3); a(n) = 12*2^(n-1) + 4*n + 2
n=3: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4); a(n) = 16*2^(n-1) + n^2 + 11*n + 8
n=4: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4); a(n) = 20*2^(n-1) + 4*n^2 + 26*n + 22
n=5: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4); a(n) = 24*2^(n-1) + 11*n^2 + 57*n + 52
n=6: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4); a(n) = 28*2^(n-1) + 26*n^2 + 120*n + 114
n=7: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4); a(n) = 32*2^(n-1) + 57*n^2 + 247*n + 240
n=8: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4); a(n) = 36*2^(n-1) + 120*n^2 + 502*n + 494
n=9: a(n) = 5*a(n-1) -9*a(n-2) +7*a(n-3) -2*a(n-4); a(n) = 40*2^(n-1) + 247*n^2 + 1013*n + 1004
EXAMPLE
Some solutions for n=4 k=4
..1..1..1..1..0....1..0..0..0..0....1..0..1..1..0....1..1..0..1..1
..1..1..1..1..0....1..1..1..1..1....1..0..1..1..0....1..1..0..1..1
..1..1..1..1..0....0..0..0..0..0....1..0..1..1..1....1..1..0..1..1
..1..1..1..1..0....0..0..0..0..1....1..0..1..1..1....1..1..0..1..1
..0..0..0..0..1....0..0..0..0..1....1..0..1..1..1....1..1..0..1..1
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 27 2014
STATUS
approved