A190036 Number of nondecreasing arrangements of n+2 numbers in 0..4 with the last equal to 4 and each after the second equal to the sum of one or two of the preceding three.

7, 12, 18, 27, 39, 53, 69, 87, 107, 129, 153, 179, 207, 237, 269, 303, 339, 377, 417, 459, 503, 549, 597, 647, 699, 753, 809, 867, 927, 989, 1053, 1119, 1187, 1257, 1329, 1403, 1479, 1557, 1637, 1719, 1803, 1889, 1977, 2067, 2159, 2253, 2349, 2447, 2547, 2649

Offset

1,1

Comments

Column 4 of A190041.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = n^2 + 3*n - 1 for n>3.

Conjectures from Colin Barker, May 04 2018: (Start)

G.f.: x*(7 - 9*x + 3*x^2 + 2*x^3 - x^5) / (1 - x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>4.

(End)

Example

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

Crossrefs

Cf. A190041.

Sequence in context: A247159 A022953 A030714 * A061141 A256381 A272975

Adjacent sequences: A190033 A190034 A190035 * A190037 A190038 A190039

Keyword

nonn

Author

R. H. Hardin, May 04 2011

Status

approved