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A009692
Number of partitions of {1, 2, ..., 2n} into pairs whose differences are primes.
4
1, 0, 1, 3, 10, 40, 153, 921, 5144, 30717, 230748, 1766056, 14052445, 116580521, 897876519, 7657321097, 75743979608, 788733735080, 7569825650083, 75242386295617, 831978453306391, 9444103049405370, 120064355466770831, 1579842230380587833
OFFSET
0,4
EXAMPLE
a(3) = 3: {{1,6}, {2,4}, {3,5}}, {{1,4}, {2,5}, {3,6}}, {{1,3}, {2,5}, {4,6}}. - Alois P. Heinz, Nov 15 2016
MAPLE
b:= proc(s) option remember; `if`(s={}, 1, (j-> add(`if`(i<j
and isprime(j-i), b(s minus {i, j}), 0), i=s))(max(s)))
end:
a:= n-> b({$1..2*n}):
seq(a(n), n=0..12); # Alois P. Heinz, Nov 15 2016
MATHEMATICA
b[s_] := b[s] = If[s == {}, 1, Function[j, Sum[If[i < j && PrimeQ[j - i], b[s ~Complement~ {i, j}], 0], {i, s}]][Max[s]]];
a[n_] := b[Range[2n]];
Table[Print[n, " ", a[n]]; a[n], {n, 0, 18}] (* Jean-François Alcover, Mar 01 2021, after Alois P. Heinz *)
CROSSREFS
Cf. A000341.
Sequence in context: A099763 A318118 A149052 * A149053 A149054 A149055
KEYWORD
nonn,hard
EXTENSIONS
a(0), a(14)-a(18) from Alois P. Heinz, Nov 15 2016
a(19)-a(23) from Bert Dobbelaere, Feb 20 2020
STATUS
approved