A202119 Number of -3..3 arrays of n elements with first, second and third differences also in -3..3.

7, 37, 153, 475, 1509, 4763, 15101, 47889, 151833, 481519, 1527001, 4842421, 15356565, 48699233, 154436377, 489754155, 1553125143, 4925322519, 15619350977, 49532617623, 157079520865, 498135926335, 1579705609759, 5009616203811

Offset

1,1

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Robert Israel, Maple-assisted proof of empirical formula

Formula

Empirical: a(n) = 4*a(n-1) -5*a(n-2) +13*a(n-3) -19*a(n-4) +14*a(n-5) -32*a(n-6) +8*a(n-7) +4*a(n-8) +24*a(n-9) +27*a(n-10) +26*a(n-11) -48*a(n-12) -29*a(n-13) -56*a(n-14) -55*a(n-15) +134*a(n-16) -80*a(n-17) +244*a(n-18) -170*a(n-19) +149*a(n-20) -175*a(n-21) +70*a(n-22) -68*a(n-23) +32*a(n-24) -22*a(n-25) +2*a(n-26) -8*a(n-27) +a(n-28) +2*a(n-29) +2*a(n-30) for n>35.

Empirical formula verified: see link. - Robert Israel, Sep 22 2019

Example

Some solutions for n=7
..2....2....1....3....3....2...-3....2....2....2...-1....0...-2...-3....2....0
..0....2....1....1....3....0...-2....2....2...-1....0...-1...-2...-3....3...-1
..0....2...-1....1....3....1....0....1....1...-2....0...-3...-2...-3....1....1
..1....1...-2....2....3....3....1...-1....0...-1...-1...-3...-1...-3...-1....3
..2....0...-2....1....3....3....1...-1...-2....0...-1...-3....1...-1....0....3
..3...-2...-3...-1....0....1....0...-1...-3....0...-1...-2....2....1....1....3
..2...-3...-3...-2...-3...-2...-3...-3...-1....0...-1....1....0....3....3....1

Crossrefs

Column 3 of A202124.

Sequence in context: A196574 A094729 A202659 * A201083 A036678 A085720

Adjacent sequences: A202116 A202117 A202118 * A202120 A202121 A202122

Keyword

nonn

Author

R. H. Hardin, Dec 11 2011

Status

approved