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A247533
T(n,k)=Number of length n+3 0..k arrays with some disjoint pairs in every consecutive four terms having the same sum
13
8, 33, 8, 88, 45, 8, 185, 136, 61, 8, 336, 317, 220, 81, 8, 553, 600, 561, 364, 105, 8, 848, 1033, 1124, 1007, 604, 153, 8, 1233, 1616, 2009, 2164, 1823, 1018, 217, 8, 1720, 2409, 3220, 3997, 4228, 3455, 1732, 297, 8, 2321, 3400, 4901, 6584, 8051, 8440, 6495, 2956
OFFSET
1,1
COMMENTS
Table starts
.8..33...88...185....336....553....848....1233....1720....2321....3048....3913
.8..45..136...317....600...1033...1616....2409....3400....4661....6168....8005
.8..61..220...561...1124...2009...3220....4901....7016....9737...13000...17025
.8..81..364..1007...2164...3997...6584...10219...14852...20847...28108...37095
.8.105..604..1823...4228...8051..13668...21609...31924...45309...61740...82067
.8.153.1018..3455...8440..16683..29012...47061...70374..101211..139098..186709
.8.217.1732..6495..16932..34695..62108..103013..156308..227701..316236..428111
.8.297.2956.12105..34068..72269.133716..226309..349160..515043..723892..987667
.8.393.5050.22459..68688.150677.288996..498569..783568.1170169.1665908.2290065
.8.585.8638.43255.139040.318575.627654.1111891.1772920.2686215.3862654.5366083
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = a(n-1) +4*a(n-4) -4*a(n-5)
k=3: a(n) = 2*a(n-1) -a(n-3) +a(n-4) -a(n-5) -a(n-6) +a(n-7)
k=4: [order 29] for n>30
k=5: [order 56]
k=6: [order 82] for n>84
Empirical for row n:
n=1: a(n) = 2*n^3 + 3*n^2 + 2*n + 1
n=2: a(n) = 2*a(n-1) +a(n-2) -4*a(n-3) +a(n-4) +2*a(n-5) -a(n-6); also a polynomial of degree 3 plus a linear quasipolynomial with period 2
n=3: [recurrence of order 12; also a polynomial of degree 3 plus a linear quasipolynomial with period 12]
n=4: [recurrence of order 24; also a polynomial of degree 3 plus a linear quasipolynomial with period 420]
n=5: [recurrence of order 48; also a polynomial of degree 3 plus a linear quasipolynomial with period 27720; note 2 12 420 27720 matches A060942]
n=6: [recurrence of order 92]
EXAMPLE
Some solutions for n=6 k=4
..2....3....2....1....4....3....3....0....2....1....0....3....1....4....1....1
..1....2....1....2....1....2....2....1....4....1....0....0....3....2....2....4
..0....3....3....2....0....2....2....2....3....2....1....2....4....1....1....1
..3....2....2....1....3....1....3....3....1....2....1....1....2....3....2....4
..4....3....2....3....2....1....3....0....2....3....2....1....3....2....3....1
..1....2....3....2....1....2....4....1....2....1....0....2....3....4....4....4
..2....3....3....2....2....2....2....2....3....0....1....0....4....3....3....1
..3....4....4....1....3....3....3....1....1....2....3....1....4....3....2....4
..4....1....2....3....4....3....1....0....2....3....4....1....3....4....1....1
CROSSREFS
Row 1 is A212133(n+1)
Sequence in context: A166995 A079271 A336220 * A240547 A031445 A131547
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Sep 18 2014
STATUS
approved