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A322600 a(n) is the number of unlabeled rank-3 graded lattices with 5 coatoms and n atoms. 4
1, 5, 20, 68, 190, 441, 907, 1690, 2916, 4734, 7310, 10836, 15528, 21619, 29365, 39045, 50961, 65434, 82809, 103453, 127751, 156117, 188980, 226794, 270037, 319204, 374813, 437409, 507553, 585831, 672847, 769233, 875637, 992735, 1121218, 1261802 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Jukka Kohonen, Table of n, a(n) for n = 1..1000

J. Kohonen, Counting graded lattices of rank three that have few coatoms, arXiv:1804.03679 [math.CO] preprint (2018).

FORMULA

For n>=3: a(n) = (175/192)n^4 - (3079/480)n^3 + (11771/480)n^2

  - [7268/160, 7273/160]n

  + [33600, 34019, 34072, 33627, 33152, 34915, 33624, 33947, 33472, 33507,

  34520, 34459, 32832, 33827, 34072, 34395, 33344, 34147, 33432, 33947,

  34240, 33699, 33752, 34267, 32832, 34595, 34264, 33627, 33152, 34147,

  34200, 34139, 33472, 33507, 33752, 35035, 33024, 33827, 34072, 33627,

  33920, 34339, 33432, 33947, 33472, 34275, 33944, 34267, 32832, 33827,

  34840, 33819, 33152, 34147, 33432, 34715, 33664, 33507, 33752, 34267] / 960.

  The value of the first bracket depends on whether n is even or odd. The value of the second bracket depends on whether (n mod 60) is 0, 1, 2, ..., 59.

Conjectures from Colin Barker, Dec 20 2018: (Start)

G.f.: x*(1 + 4*x + 14*x^2 + 43*x^3 + 102*x^4 + 184*x^5 + 282*x^6 + 368*x^7 + 411*x^8 + 400*x^9 + 333*x^10 + 237*x^11 + 142*x^12 + 70*x^13 + 26*x^14 + 7*x^15 + x^16) / ((1 - x)^5*(1 + x)^2*(1 + x^2)*(1 + x + x^2)*(1 + x + x^2 + x^3 + x^4)).

a(n) = a(n-1) + a(n-2) - a(n-5) - a(n-6) - a(n-7) + a(n-8) + a(n-9) + a(n-10) - a(n-13) - a(n-14) + a(n-15) for n>15.

(End)

CROSSREFS

Fifth row of A300260.

Previous rows are A322598, A322599.

Sequence in context: A271599 A032286 A097552 * A084850 A270169 A007327

Adjacent sequences:  A322597 A322598 A322599 * A322601 A322602 A322603

KEYWORD

nonn,easy

AUTHOR

Jukka Kohonen, Dec 19 2018

STATUS

approved

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Last modified April 25 00:29 EDT 2019. Contains 322446 sequences. (Running on oeis4.)