OFFSET
1,1
COMMENTS
Table starts
...8....27.....64.....125......216.......343........512........729........1000
..14....67....204.....485......986......1799.......3032.......4809........7270
..24...162....632....1827.....4368......9156......17424......30789.......51304
..41...391...1959....6902....19446.....46914.....100962.....199023......365959
..68...900...5696...24125....79200....217856.....526032....1149057.....2318140
.111..2026..16104...81664...311498....974944....2637228....6376143....14100493
.180..4530..45232..274901..1219944...4350588...13201680...35373129....85849852
.289..9975.124249..899306..4617079..18667931...63266403..187131076...496682670
.460.21694.335328.2878124.17036428..77880418..294117016..958537837..2777976392
.728.46871.897523.9128858.62297886.322089271.1356124591.4872648817.15429444696
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..9999
FORMULA
Empirical for column k, apparently a recurrence of order 7*k-1:
k=1: a(n) = 2*a(n-1) -a(n-2) +2*a(n-3) -2*a(n-4) -a(n-6)
k=2: [order 13]
k=3: [order 20]
k=4: [order 27]
k=5: [order 34]
k=6: [order 41]
k=7: [order 48]
Empirical for row n, apparently a polynomial of degree n+2:
n=1: a(n) = n^3 + 3*n^2 + 3*n + 1
n=2: a(n) = (2/3)*n^4 + (10/3)*n^3 + (16/3)*n^2 + (11/3)*n + 1
n=3: a(n) = (13/30)*n^5 + 3*n^4 + (22/3)*n^3 + 8*n^2 + (127/30)*n + 1
n=4: [polynomial of degree 6]
n=5: [polynomial of degree 7]
n=6: [polynomial of degree 8]
n=7: [polynomial of degree 9]
EXAMPLE
Some solutions for n=5 k=4
..4....0....3....2....2....0....1....2....3....0....0....1....0....0....2....3
..0....2....3....4....3....1....3....3....0....2....2....3....0....3....4....2
..4....1....2....2....0....1....4....1....0....0....0....1....1....4....2....2
..4....3....3....3....2....2....1....2....1....1....3....1....3....4....0....0
..1....2....3....4....2....1....3....3....0....1....2....3....0....0....4....3
..4....3....2....2....4....4....3....4....2....4....0....1....3....4....4....4
..4....4....4....3....4....2....3....4....3....0....3....1....3....4....2....0
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Nov 13 2014
STATUS
approved