A084871 Number of 4-multiantichains of an n-set.
1, 2, 7, 41, 398, 6177, 128232, 2881531, 62769238, 1288737197, 25012685732, 463681018671, 8294783320578, 144410750517217, 2462999084589232, 41359616334934211, 686406989350511918, 11290725888842193237
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..825
- Goran Kilibarda and Vladeta Jovovic, Antichains of Multisets, J. Integer Seqs., Vol. 7, 2004.
Programs
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Magma
[(16^n - 12*12^n + 24*10^n + 4*9^n - 6*8^n + 6*7^n - 108*6^n + 108*5^n + 83*4^n - 166*3^n + 90*2^n)/24: n in [0..50]]; // G. C. Greubel, Oct 08 2017
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Mathematica
Table[(16^n - 12*12^n + 24*10^n + 4*9^n - 6*8^n + 6*7^n - 108*6^n + 108*5^n + 83*4^n - 166*3^n + 90*2^n)/4!, {n, 0, 50}] (* G. C. Greubel, Oct 08 2017 *) -
PARI
for(n=0,50, print1((16^n - 12*12^n + 24*10^n + 4*9^n - 6*8^n + 6*7^n - 108*6^n + 108*5^n + 83*4^n - 166*3^n + 90*2^n)/4!, ", ")) \\ G. C. Greubel, Oct 08 2017
Formula
a(n) = (16^n - 12*12^n + 24*10^n + 4*9^n - 6*8^n + 6*7^n - 108*6^n + 108*5^n + 83*4^n - 166*3^n + 90*2^n)/4!.
From R. J. Mathar, Jul 08 2011: (Start)
G.f.: (-1 + 80*x - 2813*x^2 + 57293*x^3 - 749139*x^4 + 6577949*x^5 - 39353597*x^6 + 158972472*x^7 - 417774220*x^8 + 651991536*x^9 - 465379200*x^10) / ( (9*x-1) *(6*x-1) *(7*x-1) *(3*x-1) *(5*x-1) *(2*x-1) *(12*x-1) *(10*x-1) *(4*x-1) *(8*x-1) *(16*x-1) ).
a(n) = 82*a(n-1) - 2970*a(n-2) + 62700*a(n-3) - 856713*a(n-4) + 7947786*a(n-5) - 51019100*a(n-6) + 226259000*a(n-7) - 678011136*a(n-8) + 1304341632*a(n-9) - 1445575680*a(n-10) + 696729600*a(n-11). (End)