A253715 Indices of centered heptagonal numbers (A069099) which are also hexagonal numbers (A000384).
1, 2160, 34417, 139317984, 2220346081, 8987960385360, 143243407002961, 579849276161764800, 9241205157168647617, 37408396193312133889584, 596187109366334725327921, 2413365271435489729590825120, 38462415164418513312636815521, 155695847083980788221510357869840
Offset: 1
Examples
2160 is in the sequence because the 2160th centered heptagonal number is 16322041, which is also the 2857th hexagonal number.
Links
- Colin Barker, Table of n, a(n) for n = 1..416
- Index entries for linear recurrences with constant coefficients, signature (1,64514,-64514,-1,1).
Programs
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Mathematica
LinearRecurrence[{1,64514,-64514,-1,1},{1,2160,34417,139317984,2220346081},20] (* Harvey P. Dale, Apr 10 2019 *) -
PARI
Vec(x*(2159*x^3+32257*x^2-2159*x-1)/((x-1)*(x^2-254*x+1)*(x^2+254*x+1)) + O(x^100))
Formula
a(n) = a(n-1)+64514*a(n-2)-64514*a(n-3)-a(n-4)+a(n-5).
G.f.: x*(2159*x^3+32257*x^2-2159*x-1) / ((x-1)*(x^2-254*x+1)*(x^2+254*x+1)).
Comments