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

1,1

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

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) +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]

Example

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

Crossrefs

Column 1 is A135491(n+3)

Column 3 is A203536(n+5)

Sequence in context: A246507 A034562 A222989 * A041372 A245951 A352869

Adjacent sequences: A245947 A245948 A245949 * A245951 A245952 A245953

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 08 2014

Status

approved