A228464 Number of arrays of maxima of three adjacent elements of some 0..n array of length 9.

44, 383, 1821, 6254, 17487, 42386, 92430, 185727, 349558, 623513, 1063283, 1745172, 2771393, 4276212, 6433004, 9462285, 13640784, 19311619, 26895641, 36904010, 49952067, 66774566, 88242330, 115380395, 149387706, 191658429, 243804943

Offset

1,1

Comments

See A228461 for explanation of definition.

Links

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

Formula

Empirical: a(n) = (4/315)*n^7 + (1/5)*n^6 + (91/45)*n^5 + (63/8)*n^4 + (2557/180)*n^3 + (517/40)*n^2 + (2419/420)*n + 1 = (n+1) *(n+2) *(32*n^5 + 408*n^4 + 3808*n^3 + 7605*n^2 + 5367*n + 1260)/2520.

Conjectures from Colin Barker, Mar 16 2018: (Start)

G.f.: x*(44 + 31*x - 11*x^2 - 54*x^3 + 75*x^4 - 28*x^5 + 8*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)

Example

Some solutions for n=4:
  3   0   3   4   4   3   3   4   3   4   2   3   2   0   3   2
  3   0   2   4   4   0   0   2   1   3   4   3   0   0   4   0
  0   0   2   4   0   2   0   2   4   4   4   3   4   0   4   2
  0   0   1   3   1   3   1   2   4   4   4   3   4   4   4   2
  0   0   3   1   1   3   2   2   4   4   0   1   4   4   0   2
  1   0   3   0   4   4   3   2   4   4   0   1   0   4   3   2
  1   3   4   3   4   4   3   1   0   2   1   2   0   3   3   0

Crossrefs

Row 7 of A228461. Cf. A217949.

Sequence in context: A200450 A024304 A190420 * A190605 A264555 A231217

Adjacent sequences: A228461 A228462 A228463 * A228465 A228466 A228467

Keyword

nonn

Author

R. H. Hardin, Aug 22 2013

Status

approved