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A228260 T(n,k)=Number of third differences of arrays of length n+3 of numbers in 0..k 13
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 (list; table; graph; refs; listen; history; text; internal format)
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
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: A081030 A352789 A285009 * A147459 A188559 A014004
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Aug 19 2013
STATUS
approved

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Last modified February 26 17:57 EST 2024. Contains 370352 sequences. (Running on oeis4.)