A319777 a(n) is the number of equivalence classes of triples of sets each with n or fewer elements where two triples are equivalent if the number of elements in all intersections is the same.
1, 15, 100, 436, 1459, 4069, 9929, 21871, 44426, 84494, 152171, 261749, 432906, 692102, 1074198, 1624314, 2399943, 3473337, 4934182, 6892578, 9482341, 12864643, 17232007, 22812673, 29875352, 38734384, 49755317, 63360923, 80037668, 100342652, 124911036
Offset: 0
Keywords
Examples
The triple (A, B, C) = ({1, 2}, {1, 2, 3}, {1, 4}) is equivalent to the triple (A', B', C') = ({1, 8}, {1, 4, 8}, {5, 8}) because all intersections of the sets in a triple are equal:
|A| = |{1, 2}| = 2 = |{1, 8}| = |A'|
|B| = |{1, 2, 3}| = 3 = |{1, 4, 8}| = |B'|
|C| = |{1, 4}| = 2 = |{5, 8}| = |C'|
|A & B| = |{1, 2}| = 2 = |{1, 8}| = |A' & B'|
|A & C| = |{1}| = 1 = |{8}| = |A' & C'|
|B & C| = |{1}| = 1 = |{8}| = |B' & C'|
|A & B & C| = |{1}| = 1 = |{8}| = |A' & B' & C'|
Links
- Muniru A Asiru, Table of n, a(n) for n = 0..5000
- Index entries for linear recurrences with constant coefficients, signature (7,-20,28,-14,-14,28,-20,7,-1).
Programs
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GAP
List([0..30],n->Sum([0..n],k->(15*(127+(-1)^k)+6432*k+8936*k^2+6480*k^3+2570*k^4+528*k^5+44*k^6)/1920)); # Muniru A Asiru, Sep 28 2018
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Maple
a:=n->add((15*(127+(-1)^k)+6432*k+8936*k^2+6480*k^3+2570*k^4+528*k^5+44*k^6)/1920,k=0..n): seq(a(n),n=0..30); # Muniru A Asiru, Sep 28 2018
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PARI
a(n) = sum(k=0, n, (15*(127+(-1)^k) + 6432*k + 8936*k^2 + 6480*k^3 + 2570*k^4 + 528*k^5 + 44*k^6) / 1920); \\ Michel Marcus, Dec 27 2018
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PARI
Vec((1 + 8*x + 15*x^2 + 8*x^3 + x^4) / ((1 - x)^8*(1 + x)) + O(x^40)) \\ Colin Barker, Dec 28 2018
Formula
a(n) = Sum_{k=0..n} A244865(k). [corrected by Michel Marcus, Dec 27 2018]
From Colin Barker, Dec 27 2018: (Start)
G.f.: (1 + 8*x + 15*x^2 + 8*x^3 + x^4) / ((1 - x)^8*(1 + x)).
a(n) = 7*a(n-1) - 20*a(n-2) + 28*a(n-3) - 14*a(n-4) - 14*a(n-5) + 28*a(n-6) - 20*a(n-7) + 7*a(n-8) - a(n-9) for n>8.
(End)
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