A316220 Number of triangles whose weight is the n-th Fermi-Dirac prime in the multiorder of integer partitions of Fermi-Dirac primes into Fermi-Dirac primes.

1, 1, 3, 3, 9, 21, 46, 95, 273, 363, 731, 3088, 6247, 24152, 46012, 319511, 1141923, 2138064, 7346404, 13530107, 45297804, 271446312

Offset

1,3

Comments

A Fermi-Dirac prime (A050376) is a number of the form p^(2^k) where p is prime and k >= 0. An FD-partition is an integer partition of a Fermi-Dirac prime into Fermi-Dirac primes. a(n) is the number of sequences of FD-partitions whose sums are weakly decreasing and sum to the n-th Fermi-Dirac prime.

Links

Table of n, a(n) for n=1..22.

Gus Wiseman, Comcategories and Multiorders

Gus Wiseman, Illustration of the first six terms of A316220.

Mathematica

nn=60;
FDpQ[n_]:=With[{f=FactorInteger[n]}, n>1&&Length[f]==1&&MatchQ[FactorInteger[2f[[1, 2]]], {{2, _}}]];
FDpl=Select[Range[nn], FDpQ];
fen[n_]:=fen[n]=SeriesCoefficient[Product[1/(1-x^p), {p, Select[Range[n], FDpQ]}], {x, 0, n}];
Table[Sum[Times@@fen/@p, {p, Select[IntegerPartitions[FDpl[[n]]], And@@FDpQ/@#&]}], {n, Length[FDpl]}]

Crossrefs

Cf. A050376, A063834, A064547, A213925, A269134, A281113, A299757, A305829, A316202, A316210, A316211, A316219, A316228.

Sequence in context: A222444 A206492 A007683 * A059728 A257180 A184694

Adjacent sequences: A316217 A316218 A316219 * A316221 A316222 A316223

Keyword

nonn,more

Author

Gus Wiseman, Jun 26 2018

Status

approved