A189328 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 four.

2, 8, 11, 20, 21, 36, 31, 49, 42, 63, 51, 79, 60, 93, 72, 105, 80, 125, 89, 133, 104, 149, 109, 168, 117, 178, 135, 190, 138, 213, 147, 219, 166, 234, 166, 257, 176, 263, 197, 274, 196, 303, 205, 304, 227, 319, 225, 346, 234, 347, 259, 360, 254, 392, 262, 389, 290, 404

Offset

1,1

Comments

Row 3 of A189326.

Links

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

Formula

Empirical: a(n) = -3*a(n-1) -5*a(n-2) -5*a(n-3) -2*a(n-4) +3*a(n-5) +8*a(n-6) +10*a(n-7) +8*a(n-8) +3*a(n-9) -2*a(n-10) -5*a(n-11) -5*a(n-12) -3*a(n-13) -a(n-14).

Empirical g.f.: x*(2 + 14*x + 45*x^2 + 103*x^3 + 180*x^4 + 264*x^5 + 326*x^6 + 350*x^7 + 322*x^8 + 258*x^9 + 173*x^10 + 97*x^11 + 40*x^12 + 11*x^13) / ((1 - x)^2*(1 + x)^2*(1 + x^2)*(1 + x + x^2)^2*(1 + x + x^2 + x^3 + x^4)). - Colin Barker, May 02 2018

Example

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

Crossrefs

Cf. A189326.

Sequence in context: A074263 A295070 A009420 * A090746 A362869 A234924

Adjacent sequences: A189325 A189326 A189327 * A189329 A189330 A189331

Keyword

nonn

Author

R. H. Hardin, Apr 20 2011

Status

approved