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

Author

R. H. Hardin, Sep 18 2014

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Row 1 is A212133(n+1)

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]