A294812 Let b(n) be the number of permutations {c_1..c_n} of {1..n} for which c_1 - c_2 + ... + (-1)^(n-1)*c_n are pentagonal numbers (A000326). Then a(n) = b(n)/A010551(n).
1, 1, 1, 2, 4, 5, 6, 10, 23, 38, 70, 110, 196, 346, 759, 1250, 2313, 3982, 8433, 14520, 29437, 50466, 102830, 179587, 376439, 654374, 1343540, 2352149, 4916286, 8654120, 18065200, 31783592, 66233160, 117371504, 246610521, 436972949, 913862320, 1626523783
Offset: 1
Keywords
Links
- Peter J. C. Moses, Table of n, a(n) for n = 1..200
Programs
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Mathematica
polyQ[order_,n_]:=If[n==0,True,IntegerQ[(#-4+Sqrt[(#-4)^2+8 n (#-2)])/(2 (#-2))]&[order]];(*is a number polygonal?*) Map[Total,Table[ possibleSums=Range[1/2-(-1)^n/2-Floor[n/2]^2,Floor[(n+1)/2]^2]; filteredSums=Select[possibleSums,polyQ[5,#]&&#>-1&]; positions=Map[Flatten[{#,Position[possibleSums,#,1]-1}]&,filteredSums]; Map[SeriesCoefficient[QBinomial[n,Floor[(n+1)/2],q],{q,0,#[[2]]/2}]&,positions],{n,25}]] (* Peter J. C. Moses, Jan 02 2018 *)
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