A245869 T(n,k)=Number of length n+2 0..k arrays with some pair in every consecutive three terms totalling exactly k

6, 19, 10, 36, 45, 16, 61, 100, 103, 26, 90, 193, 256, 239, 42, 127, 318, 549, 676, 553, 68, 168, 493, 960, 1629, 1764, 1281, 110, 217, 712, 1579, 3102, 4753, 4624, 2967, 178, 270, 993, 2368, 5515, 9726, 13961, 12100, 6873, 288, 331, 1330, 3433, 8840, 18505, 30900

Offset

1,1

Comments

Table starts

.....6.......19........36.........61..........90..........127..........168

....10.......45.......100........193.........318..........493..........712

....16......103.......256........549.........960.........1579.........2368

....26......239.......676.......1629........3102.........5515.........8840

....42......553......1764.......4753........9726........18505........31176

....68.....1281......4624......13961.......30900........63241.......113024

...110.....2967.....12100......40901.......97602.......214315.......404264

...178.....6873.....31684.....119953......309078.......729097......1455496

...288....15921.....82944.....351649......977664......2475985......5223552

...466....36881....217156....1031057.....3094038......8415217.....18775816

...754....85435....568516....3022933.....9789654.....28590415.....67437448

..1220...197911...1488400....8863117....30977796.....97151683....242306240

..1974...458463...3896676...25986061....98020170....330100459....870461352

..3194..1062035..10201636...76189749...310161870...1121650903...3127322696

..5168..2460217..26708224..223384017...981426624...3811203385..11235107264

..8362..5699123..69923044..654949861..3105480558..12950003383..40363689352

.13530.13202089.183060900.1920277409..9826505742..44002376953.145010699592

.21892.30582803.479259664.5630150189.31093507092.149514426895.520968428032

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)

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

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

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

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

k=6: a(n) = 3*a(n-1) +3*a(n-2) -a(n-3) -9*a(n-4) -24*a(n-5) +5*a(n-6)

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

k=8: a(n) = 3*a(n-1) +5*a(n-2) -a(n-3) -13*a(n-4) -48*a(n-5) +7*a(n-6)

k=9: a(n) = 2*a(n-1) +8*a(n-2) -a(n-3)

Empirical for row n:

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

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

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

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

n=5: 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=6: 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=7: a(n) = 2*a(n-1) +3*a(n-2) -8*a(n-3) -2*a(n-4) +12*a(n-5) -2*a(n-6) -8*a(n-7) +3*a(n-8) +2*a(n-9) -a(n-10)

Example

Some solutions for n=6 k=4
..1....4....0....4....0....1....2....3....1....2....0....3....3....0....2....4
..4....2....1....1....4....2....4....1....0....3....1....0....3....4....1....3
..0....2....4....0....3....2....0....3....3....1....3....1....1....2....3....1
..4....0....0....4....0....1....4....0....1....1....1....3....0....0....4....3
..4....2....4....4....4....2....1....4....4....3....2....1....4....4....1....2
..0....2....0....0....3....2....0....0....0....3....2....2....4....3....0....2
..2....0....4....4....0....1....4....4....3....1....4....3....0....1....4....2
..4....4....0....1....1....2....3....0....1....4....0....1....0....2....1....2

Crossrefs

Column 1 is A006355(n+4)

Column 3 is A206981(n+2)

Row 1 is A090381.

Sequence in context: A119813 A370716 A119986 * A370155 A184197 A173568

Adjacent sequences: A245866 A245867 A245868 * A245870 A245871 A245872

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 04 2014

Status

approved