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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
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A019298(n) is the analogous sequence if the three sets must each have exactly n elements.

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).

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)

EXAMPLE

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'|

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

PROG

(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

(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

(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

CROSSREFS

Cf. A019298, A244865.

Cf. A000330(n-1) is analogous, but with pairs instead of triples.

Sequence in context: A000973 A034266 A087661 * A242657 A163717 A111370

Adjacent sequences:  A319774 A319775 A319776 * A319778 A319779 A319780

KEYWORD

nonn

AUTHOR

Peter Kagey, Sep 26 2018

STATUS

approved

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Last modified June 29 12:30 EDT 2022. Contains 354913 sequences. (Running on oeis4.)