A190043 Number of nondecreasing arrangements of 6 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, 10, 14, 27, 23, 47, 31, 65, 49, 76, 52, 113, 58, 109, 92, 132, 78, 167, 87, 172, 127, 172, 108, 240, 116, 208, 167, 237, 133, 292, 143, 272, 205, 271, 169, 366, 167, 307, 244, 348, 189, 407, 198, 377, 290, 369, 218, 493, 223, 413, 322, 445, 244, 528, 263, 482, 358, 468

Offset

1,1

Comments

Row 4 of A190041.

Links

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

Formula

Empirical: a(n) = -4*a(n-1) -11*a(n-2) -23*a(n-3) -40*a(n-4) -59*a(n-5) -75*a(n-6) -81*a(n-7) -71*a(n-8) -42*a(n-9) +4*a(n-10) +59*a(n-11) +112*a(n-12) +150*a(n-13) +164*a(n-14) +150*a(n-15) +112*a(n-16) +59*a(n-17) +4*a(n-18) -42*a(n-19) -71*a(n-20) -81*a(n-21) -75*a(n-22) -59*a(n-23) -40*a(n-24) -23*a(n-25) -11*a(n-26) -4*a(n-27) -a(n-28).

Empirical g.f.: x*(2 + 18*x + 76*x^2 + 239*x^3 + 595*x^4 + 1276*x^5 + 2393*x^6 + 4053*x^7 + 6246*x^8 + 8890*x^9 + 11721*x^10 + 14448*x^11 + 16654*x^12 + 18046*x^13 + 18363*x^14 + 17598*x^15 + 15834*x^16 + 13401*x^17 + 10606*x^18 + 7850*x^19 + 5387*x^20 + 3421*x^21 + 1976*x^22 + 1037*x^23 + 476*x^24 + 189*x^25 + 59*x^26 + 14*x^27) / ((1 - x)^2*(1 + x)^2*(1 - x + x^2)*(1 + x^2)^2*(1 + x + x^2)^2*(1 + x + x^2 + x^3 + x^4)^2*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). - Colin Barker, May 04 2018

Example

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

Crossrefs

Cf. A190041.

Sequence in context: A290143 A160773 A217191 * A217681 A102340 A358749

Adjacent sequences: A190040 A190041 A190042 * A190044 A190045 A190046

Keyword

nonn

Author

R. H. Hardin, May 04 2011

Status

approved