A203536 -id:A203536 - cp's OEIS frontend

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

R. H. Hardin, Aug 08 2014

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

			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

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

Column 1 is A135491(n+3)

Column 3 is A203536(n+5)

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]

cp's OEIS Frontend

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

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