A228218 -id:A228218 - cp's OEIS frontend

A228223 Number of second differences of arrays of length 8 of numbers in 0..n.

255, 6305, 58975, 320481, 1225631, 3693505, 9399615, 21108545, 43067071, 81457761, 144913055, 245089825, 397304415, 621228161, 941643391, 1389259905, 2001591935, 2823895585, 3910166751, 5324199521, 7140705055, 9446490945

Offset: 1

R. H. Hardin, Aug 16 2013

nonn

			Some solutions for n=4:
.-4...-4...-8...-2...-2....0....0...-4....0...-6...-4....0...-6...-2...-4...-4
.-1....7....5....4....1....0...-4...-3....0....0....7...-4....6....3....0....7
..4...-5....1...-6...-2...-3....8....2....1....5...-6....3...-4...-1....2...-6
.-2....2...-2....3....0....5...-4....2...-4...-6....1...-2....1...-1....0....4
.-2...-4....0....0...-1...-3...-1...-2....4....7....4....1...-1...-2....3....1
..2....4....1....2....3...-2....2....4...-1...-4...-5...-1....0....0...-6...-3

R. H. Hardin, Table of n, a(n) for n = 1..34

Row 6 of A228218.

Empirical: a(n) = 84*n^6 - 402*n^4 + 1656*n^3 - 1860*n^2 + 776*n + 1.
Conjectures from Colin Barker, Sep 10 2018: (Start)
G.f.: x*(255 + 4520*x + 20195*x^2 + 31136*x^3 + 8989*x^4 - 4616*x^5 + x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)

A228224 Number of second differences of arrays of length 9 of numbers in 0..n.

Original entry on oeis.org

511, 19171, 242461, 1688101, 8006491, 29066311, 86929081, 224817481, 519682231, 1098972331, 2162213461, 4007999341, 7067000851, 11941597711, 19452737521, 30694626961, 47097859951, 70501587571, 103235334541, 148211067061

Offset: 1

R. H. Hardin, Aug 16 2013

nonn

			Some solutions for n=4:
.-6...-4...-8...-6...-4...-6...-6...-6...-4...-6...-6...-6...-4...-6...-4...-4
..2....2....7....6....0....5....1....6...-4....6....4....7...-2....5....2...-4
..5....2...-6...-4....0....2....0...-3....6...-4...-3...-5....4....0...-4....8
.-4...-2....3....1....3...-4....3....0...-1....1....6....3...-2...-3....5...-7
.-3....0....0...-3...-5....1...-3...-3...-1...-1...-4...-3...-1....2...-3....3
..3....2....0....3....3....0....1....3....1....4...-3....3....2...-3....0....0
.-1...-2....2....0....1...-2....0....1...-4...-4....4...-2...-4....0....4....0

R. H. Hardin, Table of n, a(n) for n = 1..24

Row 7 of A228218.

Empirical: a(n) = 120*n^7 - 42*n^6 - 1158*n^5 + 6945*n^4 - 13980*n^3 + 13512*n^2 - 4887*n + 1.
Conjectures from Colin Barker, Sep 10 2018: (Start)
G.f.: x*(511 + 15083*x + 103401*x^2 + 256585*x^3 + 252785*x^4 + 16749*x^5 - 40313*x^6 - x^7) / (1 - x)^8.
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
(End)

cp's OEIS Frontend

A228223 Number of second differences of arrays of length 8 of numbers in 0..n.

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