A228218 T(n,k)=Number of second differences of arrays of length n+2 of numbers in 0..k

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

R. H. Hardin, Table of n, a(n) for n = 1..310

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

Adjacent sequences: A228215 A228216 A228217 * A228219 A228220 A228221

Keyword

nonn,tabl

Author

R. H. Hardin Aug 16 2013

Status

approved