A190042 Number of nondecreasing arrangements of 5 numbers in 0..n with the last equal to n and each after the second equal to the sum of one or two of the preceding three.

2, 8, 10, 18, 16, 30, 22, 40, 31, 49, 36, 64, 41, 71, 53, 81, 55, 97, 61, 103, 74, 112, 75, 131, 80, 134, 96, 144, 94, 164, 100, 166, 117, 175, 114, 198, 119, 197, 139, 207, 133, 231, 139, 229, 160, 238, 153, 265, 158, 260, 182, 270, 172, 298, 178, 292, 203, 301, 192

Offset

1,1

Comments

Row 3 of A190041.

Links

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

Formula

Empirical: a(n) = -2*a(n-1) -2*a(n-2) +3*a(n-4) +4*a(n-5) +3*a(n-6) -2*a(n-8) -2*a(n-9) -a(n-10).

Empirical g.f.: x*(2 + 12*x + 30*x^2 + 54*x^3 + 66*x^4 + 66*x^5 + 46*x^6 + 26*x^7 + 9*x^8 + 3*x^9) / ((1 - x)^2*(1 + x)^2*(1 + x^2)*(1 + x + x^2)^2). - Colin Barker, May 04 2018

Example

All solutions for n=3:
..1....1....1....3....0....1....1....0....2....1
..1....1....3....3....3....2....2....1....3....1
..1....2....3....3....3....3....2....1....3....2
..2....2....3....3....3....3....3....2....3....3
..3....3....3....3....3....3....3....3....3....3

Crossrefs

Cf. A190041.

Sequence in context: A226831 A197115 A288824 * A297293 A294157 A082396

Adjacent sequences: A190039 A190040 A190041 * A190043 A190044 A190045

Keyword

nonn

Author

R. H. Hardin, May 04 2011

Status

approved