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