login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; table; graph; refs; listen; history; text; internal format)
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

Sequence in context: A107980 A163161 A188358 * A314993 A314994 A106503

Adjacent sequences:  A228215 A228216 A228217 * A228219 A228220 A228221

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Aug 16 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 22 16:41 EDT 2019. Contains 327311 sequences. (Running on oeis4.)