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A335649
a(n) is the frequency of multi-pairs in a sequence of multi-set designs with 2 blocks.
1
0, 10, 200, 3040, 43320, 607050, 8468880, 118007680, 1643826800, 22896269770, 318906570840, 4441805503200, 61866406977960, 861688028423050, 12001766499380000, 167163044860403200, 2328280868627854560, 32428769142358413450, 451674487223023755240, 6291014052348080593120
OFFSET
1,2
REFERENCES
A. Assaf, A. Hartman, E. Mendelsohn, Multi-set Designs-Designs having blocks with repeated elements, Congressus Numerantium, 48 (1985), 7-24.
FORMULA
a(n) = (1/12)*((2+sqrt(3))^(2*n) + (2-sqrt(3))^(2*n) - 6*(2+sqrt(3))^n - 6*(2-sqrt(3))^n + 10).
a(n) = (1/3)*(A092184(n+1)*(A092184(n+1)-1)).
From Colin Barker, Jun 16 2020: (Start)
G.f.: 10*x^2*(1 + x) / ((1 - x)*(1 - 14*x + x^2)*(1 - 4*x + x^2)).
a(n) = 19*a(n-1) - 76*a(n-2) + 76*a(n-3) - 19*a(n-4) + a(n-5) for n>5.
(End)
EXAMPLE
For V={x,y} the design for n=2 are the blocks {xxxxxy,xyyyyy}. Pair frequencies of the multi-pairs xx, yy, and xy in these 2 blocks are all a(2)=10.
A092184(3)=6, and the above example has blocks of size 6.
MATHEMATICA
LinearRecurrence[{19, -76, 76, -19, 1}, {0, 10, 200, 3040, 43320, 607050}, 20] (* Amiram Eldar, Jun 16 2020 *)
PROG
(PARI) concat(0, Vec(10*x^2*(1 + x) / ((1 - x)*(1 - 14*x + x^2)*(1 - 4*x + x^2)) + O(x^20))) \\ Colin Barker, Jun 16 2020
CROSSREFS
A092184(n+1) is the block size of the n-th design in the sequence.
Sequence in context: A285021 A354410 A126431 * A202436 A320671 A237025
KEYWORD
nonn,easy
AUTHOR
John P. McSorley, Jun 15 2020
EXTENSIONS
More terms from Jinyuan Wang, Jun 15 2020
STATUS
approved