A247927 T(n,k)=Number of length n+4 0..k arrays with some disjoint pairs in every consecutive five terms having the same sum

32, 203, 64, 824, 529, 128, 2365, 2760, 1387, 256, 5496, 9569, 9248, 3649, 512, 11167, 25512, 38753, 31092, 9611, 1024, 20648, 57769, 118416, 157589, 104692, 25265, 2048, 35249, 117256, 298267, 552708, 641575, 352744, 66443, 4096, 56960, 216937, 663080

Offset

1,1

Comments

Table starts

....32.....203......824......2365.......5496.......11167........20648

....64.....529.....2760......9569......25512.......57769.......117256

...128....1387.....9248.....38753.....118416......298267.......663080

...256....3649....31092....157589.....552708.....1551533......3785236

...512....9611...104692....641575....2582556.....8083791.....21652632

..1024...25265...352744...2609703...12052496....42077905....123827876

..2048...66443..1189016..10628145...56329528...219338895....709026892

..4096..174817..4008988..43309569..263412952..1144120333...4062290944

..8192..460139.13519544.176541467.1232134860..5970696303..23284325652

.16384.1211409.45597176.719680843.5763691618.31162093065.133483154922

Links

R. H. Hardin, Table of n, a(n) for n = 1..2022

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

k=2: [order 12]

k=3: [order 79]

Empirical for row n:

n=1: a(n) = 2*a(n-1) -a(n-3) -2*a(n-5) +2*a(n-6) +a(n-8) -2*a(n-10) +a(n-11); also a polynomial of degree 4 plus a linear quasipolynomial with period 12

n=2: [order 27; also a polynomial of degree 5 plus a linear quasipolynomial with period 420]

Example

Some solutions for n=4 k=4
..1....2....2....1....2....2....2....1....1....3....2....1....2....0....1....2
..3....3....3....2....3....1....3....2....2....0....3....1....4....3....4....3
..1....4....4....4....4....1....4....3....3....2....2....1....0....4....0....2
..3....3....3....3....0....4....3....0....1....0....3....0....2....4....3....0
..0....2....0....3....1....4....1....1....4....1....3....1....4....0....1....1
..2....3....0....0....3....1....2....3....4....3....4....1....2....0....4....1
..3....0....4....2....0....4....0....0....3....0....2....0....1....4....2....2
..4....2....1....0....2....1....4....4....0....2....0....4....4....4....2....0

Crossrefs

Column 1 is A000079(n+4)

Sequence in context: A130811 A350740 A232051 * A247928 A184020 A283336

Adjacent sequences: A247924 A247925 A247926 * A247928 A247929 A247930

Keyword

nonn,tabl

Author

R. H. Hardin, Sep 26 2014

Status

approved