A245950 T(n,k)=Number of length n+3 0..k arrays with some pair in every consecutive four terms totalling exactly k.

14, 71, 26, 196, 197, 48, 453, 676, 545, 88, 834, 1889, 2304, 1501, 162, 1435, 3966, 7769, 7744, 4145, 298, 2216, 7669, 18384, 31465, 26244, 11441, 548, 3305, 13064, 39721, 82968, 128649, 88804, 31577, 1008, 4630, 21281, 73728, 199141, 381222

Offset: 1

Author

R. H. Hardin, Aug 08 2014

Keywords

• nonn
• tabl

Comments

Table starts

...14.....71......196.......453.......834.......1435........2216........3305

...26....197......676......1889......3966.......7669.......13064.......21281

...48....545.....2304......7769.....18384......39721.......73728......130193

...88...1501.....7744.....31465.....82968.....199141......397504......754321

..162...4145....26244....128649....381222....1021225.....2217096.....4555697

..298..11441....88804....525041...1744494....5208673....12257032....27206945

..548..31577...300304...2141609...7972932...26526337....67596992...161991665

.1008..87161..1016064...8740385..36489120..135336793...373997376...968575361

.1854.240581..3437316..35666177.166920402..690045061..2066660136..5781493025

.3410.664051.11628100.145538749.763564758.3518298991.11420014856.34510470937

Examples

			Some solutions for n=4 k=4
..1....4....0....2....1....3....3....0....3....2....0....4....0....3....2....2
..3....2....1....1....4....2....1....4....0....4....1....0....4....4....0....2
..3....2....4....3....0....2....1....1....4....1....4....3....4....2....2....2
..2....1....2....0....0....0....4....0....3....3....3....1....3....1....2....0
..1....3....0....1....3....4....3....2....2....2....0....1....0....0....2....4
..3....4....3....0....1....2....1....3....0....1....1....4....2....3....1....1
..1....2....1....4....0....3....1....2....1....4....1....0....1....1....1....4
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..9999

Crossrefs

Column 1 is A135491(n+3)

Column 3 is A203536(n+5)

Formula

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2) +a(n-3)

k=2: a(n) = 2*a(n-1) +2*a(n-2) +a(n-3) -a(n-4) -2*a(n-5) -2*a(n-6) -a(n-7) +a(n-8) +a(n-9)

k=3: a(n) = 2*a(n-1) +3*a(n-2) +6*a(n-3) -a(n-4) -a(n-6)

k=4: [order 15]

k=5: a(n) = 3*a(n-1) +5*a(n-2) +13*a(n-3) -13*a(n-4) -a(n-5) -3*a(n-6) +a(n-7)

k=6: [order 16]

k=7: a(n) = 3*a(n-1) +9*a(n-2) +31*a(n-3) -19*a(n-4) -3*a(n-5) -5*a(n-6) +a(n-7)

k=8: [order 16]

k=9: a(n) = 3*a(n-1) +13*a(n-2) +57*a(n-3) -25*a(n-4) -5*a(n-5) -7*a(n-6) +a(n-7)

Empirical for row n:

n=1: a(n) = 2*a(n-1) +a(n-2) -4*a(n-3) +a(n-4) +2*a(n-5) -a(n-6)

n=2: a(n) = 2*a(n-1) +2*a(n-2) -6*a(n-3) +6*a(n-5) -2*a(n-6) -2*a(n-7) +a(n-8)

n=3: a(n) = 3*a(n-1) -8*a(n-3) +6*a(n-4) +6*a(n-5) -8*a(n-6) +3*a(n-8) -a(n-9)

n=4: [order 10]

n=5: [order 12]

n=6: [order 13]

n=7: [order 14]