OFFSET
1,1
COMMENTS
Table starts
.8..33...88...185....336....553....848....1233....1720....2321....3048....3913
.8..45..136...317....600...1033...1616....2409....3400....4661....6168....8005
.8..61..220...561...1124...2009...3220....4901....7016....9737...13000...17025
.8..81..364..1007...2164...3997...6584...10219...14852...20847...28108...37095
.8.105..604..1823...4228...8051..13668...21609...31924...45309...61740...82067
.8.153.1018..3455...8440..16683..29012...47061...70374..101211..139098..186709
.8.217.1732..6495..16932..34695..62108..103013..156308..227701..316236..428111
.8.297.2956.12105..34068..72269.133716..226309..349160..515043..723892..987667
.8.393.5050.22459..68688.150677.288996..498569..783568.1170169.1665908.2290065
.8.585.8638.43255.139040.318575.627654.1111891.1772920.2686215.3862654.5366083
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..9999
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +4*a(n-4) -4*a(n-5)
k=3: a(n) = 2*a(n-1) -a(n-3) +a(n-4) -a(n-5) -a(n-6) +a(n-7)
k=4: [order 29] for n>30
k=5: [order 56]
k=6: [order 82] for n>84
Empirical for row n:
n=1: a(n) = 2*n^3 + 3*n^2 + 2*n + 1
n=2: a(n) = 2*a(n-1) +a(n-2) -4*a(n-3) +a(n-4) +2*a(n-5) -a(n-6); also a polynomial of degree 3 plus a linear quasipolynomial with period 2
n=3: [recurrence of order 12; also a polynomial of degree 3 plus a linear quasipolynomial with period 12]
n=4: [recurrence of order 24; also a polynomial of degree 3 plus a linear quasipolynomial with period 420]
n=5: [recurrence of order 48; also a polynomial of degree 3 plus a linear quasipolynomial with period 27720; note 2 12 420 27720 matches A060942]
n=6: [recurrence of order 92]
EXAMPLE
Some solutions for n=6 k=4
..2....3....2....1....4....3....3....0....2....1....0....3....1....4....1....1
..1....2....1....2....1....2....2....1....4....1....0....0....3....2....2....4
..0....3....3....2....0....2....2....2....3....2....1....2....4....1....1....1
..3....2....2....1....3....1....3....3....1....2....1....1....2....3....2....4
..4....3....2....3....2....1....3....0....2....3....2....1....3....2....3....1
..1....2....3....2....1....2....4....1....2....1....0....2....3....4....4....4
..2....3....3....2....2....2....2....2....3....0....1....0....4....3....3....1
..3....4....4....1....3....3....3....1....1....2....3....1....4....3....2....4
..4....1....2....3....4....3....1....0....2....3....4....1....3....4....1....1
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Sep 18 2014
STATUS
approved