OFFSET
1,1
COMMENTS
Table starts
..2.....3......4.......5........6.........7.........8..........9.........10
..4.....9.....16......25.......36........49........64.........81........100
..6....24.....60.....120......210.......336.......504........720........990
..9....63....221.....567.....1209......2279......3933.......6351.......9737
.12...159....796....2637.....6876.....15307.....30444......55641......95212
.16...396...2828...12125....38738....101999....234080.....484673.....926390
.20...969...9928...55225...216528....675151...1789528....4200933....8974480
.25..2349..34537..249600..1202353...4443665..13613507...36254755...86609789
.30..5640.119236.1120868..6639294..29104549.103118640..311698647..833022466
.36.13455.409098.5006144.36486190.189818232.778158768.2670823421.7987993868
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..9999
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1) -2*a(n-3) +a(n-4)
k=2: a(n) = 3*a(n-1) +a(n-2) -6*a(n-3)
k=3: a(n) = 9*a(n-1) -21*a(n-2) -19*a(n-3) +93*a(n-4) +27*a(n-5) -133*a(n-6) -87*a(n-7)
k=4: [order 7]
k=5: [order 13]
k=6: [order 14]
k=7: [order 16]
Empirical for row n:
n=1: a(n) = n + 1
n=2: a(n) = n^2 + 2*n + 1
n=3: a(n) = n^3 + 3*n^2 + 2*n
n=4: a(n) = n^4 + 4*n^3 + 3*n^2 + 2*n - 1
n=5: a(n) = n^5 + 5*n^4 + 4*n^3 + 6*n^2 - 5*n + 1
n=6: a(n) = n^6 + 6*n^5 + 5*n^4 + 12*n^3 - 12*n^2 + 9*n - 7 for n>2
n=7: a(n) = n^7 + 7*n^6 + 6*n^5 + 20*n^4 - 22*n^3 + 28*n^2 - 37*n + 13 for n>2
EXAMPLE
Some solutions for n=6 k=4
..4. .2. .3. .4. .3. .0. .2. .4. .0. .3. .1. .0. .4. .1. .0. .3
..0. .3. .1. .2. .1. .0. .1. .3. .0. .4. .2. .2. .1. .3. .3. .2
..3. .1. .2. .4. .4. .3. .4. .0. .1. .3. .0. .1. .0. .2. .0. .4
..2. .4. .0. .3. .2. .1. .1. .2. .2. .0. .1. .0. .3. .0. .3. .0
..1. .1. .2. .3. .2. .2. .3. .0. .4. .3. .0. .3. .2. .4. .1. .1
..0. .4. .3. .0. .4. .1. .3. .2. .2. .0. .2. .0. .4. .1. .2. .1
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 02 2016
STATUS
approved