A228744 Number of arrays of the median of three adjacent elements of some length 9 0..n array.

88, 1071, 6130, 23627, 71278, 181885, 410828, 845517, 1617004, 2913955, 4999182, 8228935, 13075154, 20150881, 30239032, 44324729, 63631392, 89660791, 124237258, 169556259, 228237526, 303382949, 398639428, 518266885, 667211636, 851185323

Offset

1,1

Comments

Row 7 of A228740.

Links

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

Formula

Empirical: a(n) = (5/126)*n^7 + (4/3)*n^6 + (829/90)*n^5 + (93/4)*n^4 + (509/18)*n^3 + (221/12)*n^2 + (453/70)*n + 1.

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

G.f.: x*(88 + 367*x + 26*x^2 - 353*x^3 + 86*x^4 - 21*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:
  2  4  0  4  3  2  0  4  1  2  3  1  4  2  1  1
  3  1  1  3  0  3  1  2  1  2  2  2  4  2  1  2
  2  4  4  2  1  0  1  4  4  3  2  4  0  3  0  3
  2  0  2  1  0  0  0  4  3  3  0  4  4  4  4  3
  2  2  4  2  0  0  0  4  4  4  2  3  2  4  4  4
  0  1  4  2  0  2  1  4  3  4  0  2  4  0  4  2
  1  1  4  2  2  4  4  1  0  2  1  2  2  0  4  4

Crossrefs

Cf. A228740.

Sequence in context: A321061 A295591 A182676 * A249294 A239274 A235018

Adjacent sequences: A228741 A228742 A228743 * A228745 A228746 A228747

Keyword

nonn

Author

R. H. Hardin, Sep 01 2013

Status

approved