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A202124 T(n,k) is the number of -k..k arrays of n elements with first, second and third differences also in -k..k. 12
3, 5, 7, 7, 19, 13, 9, 37, 57, 19, 11, 61, 153, 127, 27, 13, 91, 323, 475, 293, 35, 15, 127, 587, 1279, 1509, 663, 47, 17, 169, 967, 2833, 5205, 4763, 1517, 65, 19, 217, 1483, 5509, 14063, 21093, 15101, 3459, 91, 21, 271, 2157, 9739, 32267, 69573, 85771, 47889, 7905 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Table starts
...3.....5......7.......9.......11........13........15.........17.........19
...7....19.....37......61.......91.......127.......169........217........271
..13....57....153.....323......587.......967......1483.......2157.......3009
..19...127....475....1279.....2833......5509......9739......16039......25003
..27...293...1509....5205....14063.....32267.....65773.....122709.....213697
..35...663...4763...21093....69573....188505....443169.....936715....1822729
..47..1517..15101...85771...345241...1104357...2993875....7169025...15586785
..65..3459..47889..348841..1713419...6471075..20229855...54878469..133314467
..91..7905.151833.1418711..8503671..37917347.136692527..420086101.1140231725
.129.18051.481519.5769945.42203951.222179581.923636217.3215726871.9752442535
For fixed n, T(n,k) is the number of lattice points in k*C(n) where C(n) is a certain polytope in R^n whose vertices have rational coefficients. Therefore row n of the table is an Ehrhart quasi-polynomial of degree <= n. - Robert Israel, Jun 28 2019
LINKS
EXAMPLE
Some solutions for n=6, k=5:
3 2 -1 -5 -3 5 1 4 -2 0 3 4 -3 -3 -3 -5
-2 4 -2 0 -1 5 -3 -1 -2 1 -2 1 2 -4 -4 -4
-5 3 -2 4 1 4 -2 -2 1 3 -5 -1 3 -3 -3 0
-5 -1 -1 4 2 5 2 0 2 3 -4 -3 2 0 1 2
-2 -3 -3 4 4 5 5 2 1 1 -3 -1 1 3 5 3
3 -4 -5 0 5 0 5 5 1 0 0 1 2 2 5 2
CROSSREFS
Row 2 is A003215.
Row 3 is A007202.
Sequence in context: A099726 A327096 A202664 * A201088 A201042 A142340
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 11 2011
STATUS
approved

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Last modified July 14 18:01 EDT 2024. Contains 374322 sequences. (Running on oeis4.)