A228260 T(n,k)=Number of third differences of arrays of length n+3 of numbers in 0..k

9, 17, 31, 25, 143, 63, 33, 319, 621, 127, 41, 565, 2511, 2059, 255, 49, 881, 6419, 13933, 6305, 511, 57, 1267, 12947, 53315, 58911, 19171, 1023, 65, 1723, 22727, 141989, 315601, 242461, 58025, 2047, 73, 2249, 36471, 310425, 1161855, 1688101, 989527

Offset

1,1

Comments

Table starts

....9.....17.......25........33.........41..........49..........57...........65

...31....143......319.......565........881........1267........1723.........2249

...63....621.....2511......6419......12947.......22727.......36471........54851

..127...2059....13933.....53315.....141989......310425......596591......1045439

..255...6305....58911....315601....1161855.....3298681.....7795501.....16171769

..511..19171...242461...1688101....8003363....28791007....83538705....206640895

.1023..58025...989527...8717049...50554951...218845881...761638071...2238075697

.2047.175099..4017157..44633821..313882531..1609259287..6537612649..22217937193

.4095.527345.16245775.227363409.1932641711.11658284065.54701587935.211702564321

Links

R. H. Hardin, Table of n, a(n) for n = 1..160

Formula

Empirical for column k:

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

k=2: a(n) = 5*a(n-1) -6*a(n-2) for n>5

k=3: a(n) = 7*a(n-1) -12*a(n-2) for n>7

k=4: a(n) = 9*a(n-1) -20*a(n-2) for n>8

k=5: a(n) = 11*a(n-1) -30*a(n-2) for n>10

k=6: a(n) = 13*a(n-1) -42*a(n-2) for n>12

k=7: a(n) = 15*a(n-1) -56*a(n-2) for n>14

Empirical for row n:

n=1: a(n) = 8*n + 1

n=2: a(n) = 35*n^2 + 1*n + 1 for n>1

n=3: a(n) = 112*n^3 - 34*n^2 - 38*n - 13 for n>4

n=4: a(n) = 294*n^4 - 256*n^3 - 489*n^2 + 477*n + 415 for n>8

n=5: a(n) = 672*n^5 - 1152*n^4 - 3340*n^3 + 8908*n^2 + 4108*n - 14279 for n>13

Example

Some solutions for n=4 k=4
..3...-5....5...-6....3...-7...-8...12....9...13....9...-1....3...-8....7...10
..0....1...-4....7....0....7....3...-7..-12..-13...-3....0...-1...13...-6..-12
.-7....4....6...-7...-6...-7....4...-3...11...13...-5....4...-5..-12....8...12
.10...-8...-1....2...10...-1...-8....8...-8..-15....0...-5....7....8...-6...-9

Crossrefs

Sequence in context: A109333 A081030 A285009 * A147459 A352789 A188559

Adjacent sequences: A228257 A228258 A228259 * A228261 A228262 A228263

Keyword

nonn,tabl

Author

R. H. Hardin Aug 19 2013

Status

approved