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A245872
Number of length 3+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.
1
16, 103, 256, 549, 960, 1579, 2368, 3433, 4720, 6351, 8256, 10573, 13216, 16339, 19840, 23889, 28368, 33463, 39040, 45301, 52096, 59643, 67776, 76729, 86320, 96799, 107968, 120093, 132960, 146851, 161536, 177313, 193936, 211719, 230400, 250309
OFFSET
1,1
LINKS
FORMULA
Empirical: a(n) = 2*a(n-1) + a(n-2) - 4*a(n-3) + a(n-4) + 2*a(n-5) - a(n-6).
Conjectures from Colin Barker, Nov 04 2018: (Start)
G.f.: x*(16 + 71*x + 34*x^2 - 2*x^3 + 2*x^4 - x^5) / ((1 - x)^4*(1 + x)^2).
a(n) = 1 + 5*n + 13*n^2 + 5*n^3 for n even.
a(n) = -5 + 3*n + 13*n^2 + 5*n^3 for n odd.
(End)
EXAMPLE
Some solutions for n=10:
7 7 7 5 1 9 3 6 4 9 10 10 5 2 9 0
3 4 3 5 1 9 10 4 2 1 8 0 7 4 5 6
5 6 5 4 9 1 7 10 8 4 2 10 5 6 5 4
5 2 7 5 5 4 3 0 8 6 4 0 5 4 5 5
4 4 3 6 5 9 10 6 2 4 6 6 8 1 3 6
CROSSREFS
Row 3 of A245869.
Sequence in context: A264281 A240257 A199773 * A304505 A210687 A000739
KEYWORD
nonn
AUTHOR
R. H. Hardin, Aug 04 2014
STATUS
approved