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A228256 Number of third differences of arrays of length n+3 of numbers in 0..4. 1

%I #8 Sep 10 2018 09:53:23

%S 33,565,6419,53315,315601,1688101,8717049,44633821,227363409,

%T 1153594261,5835080169,29443836301,148292923329,745759583941,

%U 3745977788889,18798608421181,94267920012849,472439111692021,2366593604971209

%N Number of third differences of arrays of length n+3 of numbers in 0..4.

%H R. H. Hardin, <a href="/A228256/b228256.txt">Table of n, a(n) for n = 1..121</a>

%F Empirical: a(n) = 9*a(n-1) - 20*a(n-2) for n>8.

%F Conjectures from _Colin Barker_, Sep 10 2018: (Start)

%F G.f.: x*(33 + 268*x + 1994*x^2 + 6844*x^3 - 35854*x^4 - 86008*x^5 - 163840*x^6 - 57600*x^7) / ((1 - 4*x)*(1 - 5*x)).

%F a(n) = 5^(3+n) - 4^(3+n) for n>6.

%F (End)

%e Some solutions for n=4:

%e .12..-10....2...-7....8...-5....2..-13...-7..-15...-6...-3....5....3....7....2

%e .-7....8....3....6...-2....1....0...13....4....9....0....4...-2...-3..-12....3

%e .-1...-6....1....1...-1...-3...-7..-12....1....0....9...-1...-6....2...12...-1

%e ..4....8...-7...-1...-4...-2...10...12...-6...-2..-13...-3...10...-5...-6....5

%Y Column 4 of A228260.

%K nonn

%O 1,1

%A _R. H. Hardin_, Aug 19 2013

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Last modified February 23 11:40 EST 2024. Contains 370283 sequences. (Running on oeis4.)