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A175630
a(n) = n-th pentagonal number mod (n+2).
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
0,4
COMMENTS
k>=0, a(7+2*k)=7, (for odd indices >=7),
also k>=0, a(14+2*k)=15+k, (for even indices >=14).
LINKS
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)
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 *)
CROSSREFS
Cf. A000326 Pentagonal numbers:n(3n-1)/2, A179820 a(n) = n-th triangular number mod (n+2).
Sequence in context: A222757 A004568 A079904 * A021420 A330473 A198543
KEYWORD
nonn
AUTHOR
Zak Seidov, Jul 29 2010
STATUS
approved