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

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

R. H. Hardin, Table of n, a(n) for n = 1..9999

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

Adjacent sequences: A247530 A247531 A247532 * A247534 A247535 A247536

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 18 2014

Status

approved