A245872 Number of length 3+2 0..n arrays with some pair in every consecutive three terms totalling exactly n.

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

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

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

Adjacent sequences: A245869 A245870 A245871 * A245873 A245874 A245875

Keyword

nonn

Author

R. H. Hardin, Aug 04 2014

Status

approved