A201044 Number of -n..n arrays of 5 elements with adjacent element differences also in -n..n.
99, 1161, 6083, 21141, 57343, 131781, 268983, 502265, 875083, 1442385, 2271963, 3445805, 5061447, 7233325, 10094127, 13796145, 18512627, 24439129, 31794867, 40824069, 51797327, 65012949, 80798311, 99511209, 121541211, 147311009
Offset: 1
Keywords
Examples
Some solutions for n=5: .-5...-3...-4...-2...-3...-4...-1...-4...-4....5...-5...-1...-1....0...-2...-1 .-1....0...-2....2....2...-4...-2....0...-2....0...-2....0...-3....0....1....0 .-5....0....1....2...-2....1...-1...-2...-1....2...-2....2...-2...-3....0....1 ..0....5...-4...-2....3...-2...-2...-3...-2....1....1....1...-2...-5....0...-4 .-4....1...-5....1....0...-1...-4....0....0....5....0....0...-5...-2...-3...-2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A201042.
Formula
Empirical: a(n) = (169/15)*n^5 + (169/6)*n^4 + 32*n^3 + (119/6)*n^2 + (101/15)*n + 1.
Conjectures from Colin Barker, May 22 2018: (Start)
G.f.: x*(99 + 567*x + 602*x^2 + 78*x^3 + 7*x^4 - x^5) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
(End)
Comments