A175630 a(n) = n-th pentagonal number mod (n+2).
0, 1, 1, 2, 4, 0, 3, 7, 2, 7, 1, 7, 0, 7, 15, 7, 16, 7, 17, 7, 18, 7, 19, 7, 20, 7, 21, 7, 22, 7, 23, 7, 24, 7, 25, 7, 26, 7, 27, 7, 28, 7, 29, 7, 30, 7, 31, 7, 32, 7, 33, 7, 34, 7, 35, 7, 36, 7, 37, 7, 38, 7, 39, 7, 40, 7, 41, 7, 42, 7, 43, 7, 44, 7, 45, 7, 46, 7, 47, 7, 48, 7, 49, 7, 50, 7, 51
Offset: 0
Keywords
Links
- Harvey P. Dale, Table of n, a(n) for n = 0..1000
Crossrefs
Programs
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Mathematica
Table[Mod[n(3n-1)/2,n+2],{n,0,200}] With[{nn=90},Mod[PolygonalNumber[5,Range[0,nn]],Range[2,nn+2]]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jun 28 2020 *)
Formula
From Chai Wah Wu, Oct 12 2018: (Start)
a(n) = 2*a(n-2) - a(n-4) for n > 16.
G.f.: x*(-14*x^15 + 16*x^13 - 7*x^8 + 9*x^6 - 4*x^5 - 3*x^4 + 2*x^3 + x + 1)/((x - 1)^2*(x + 1)^2). (End)
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