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A228218
T(n,k)=Number of second differences of arrays of length n+2 of numbers in 0..k
13
5, 9, 15, 13, 49, 31, 17, 103, 199, 63, 21, 177, 625, 665, 127, 25, 271, 1429, 3151, 2059, 255, 29, 385, 2731, 9705, 14053, 6305, 511, 33, 519, 4651, 23351, 58141, 58975, 19171, 1023, 37, 673, 7309, 47953, 176851, 320481, 242461, 58025, 2047, 41, 847, 10825
OFFSET
1,1
COMMENTS
Table starts
....5......9......13.......17........21.........25.........29..........33
...15.....49.....103......177.......271........385........519.........673
...31....199.....625.....1429......2731.......4651.......7309.......10825
...63....665....3151.....9705.....23351......47953......88215......149681
..127...2059...14053....58141....176851.....439927.....951049.....1854553
..255...6305...58975...320481...1225631....3693505....9399615....21108545
..511..19171..242461..1688101...8006491...29066311...86929081...224817481
.1023..58025..989527..8717049..50556551..219071473..766106895..2276277137
.2047.175099.4017157.44633821.313882531.1609259287.6537612649.22222129177
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>9
k=5: a(n) = 11*a(n-1) -30*a(n-2) for n>11
k=6: a(n) = 13*a(n-1) -42*a(n-2) for n>13
k=7: a(n) = 15*a(n-1) -56*a(n-2) for n>15
Empirical for row n:
n=1: a(n) = 4*n + 1
n=2: a(n) = 10*n^2 + 4*n + 1
n=3: a(n) = 20*n^3 + 9*n^2 + 1*n + 1
n=4: a(n) = 35*n^4 + 14*n^3 - 17*n^2 + 30*n + 1
n=5: a(n) = 56*n^5 + 14*n^4 - 108*n^3 + 289*n^2 - 125*n + 1
n=6: a(n) = 84*n^6 - 402*n^4 + 1656*n^3 - 1860*n^2 + 776*n + 1
n=7: a(n) = 120*n^7 - 42*n^6 - 1158*n^5 + 6945*n^4 - 13980*n^3 + 13512*n^2 - 4887*n + 1
EXAMPLE
Some solutions for n=4 k=4
..4...-5....3...-3....6...-4...-3...-5...-8....1....5...-2....4...-3...-1...-6
.-6....7....1...-2...-6....1....4....5....6...-5...-5....1....0....0...-3....4
..2...-3...-1....5....4....2....0...-2...-2....5....7....1....0...-3....3....1
.-2...-1...-2...-1...-6....0...-4....4....1....2...-7....1....4....6...-4...-6
CROSSREFS
Row 1 is A004766. A228212 (k=2), A228213 (k=3), A228213 (k=4), A228215 (k=5).
Sequence in context: A163161 A331556 A188358 * A361993 A314993 A314994
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin Aug 16 2013
STATUS
approved