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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. 7
1, 1, 3, 3, 9, 21, 46, 95, 273, 363, 731, 3088, 6247, 24152, 46012, 319511, 1141923, 2138064, 7346404, 13530107, 45297804, 271446312 (list; graph; refs; listen; history; text; internal format)
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

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Last modified July 15 02:28 EDT 2020. Contains 335762 sequences. (Running on oeis4.)