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

1,2

Comments

Also positive integers y in the solutions to 4*x^2-7*y^2-2*x+7*y-2 = 0, the corresponding values of x being A253714.

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).

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)).

Example

2160 is in the sequence because the 2160th centered heptagonal number is 16322041, which is also the 2857th hexagonal number.

Mathematica

LinearRecurrence[{1, 64514, -64514, -1, 1}, {1, 2160, 34417, 139317984, 2220346081}, 20] (* Harvey P. Dale, Apr 10 2019 *)

Prog

(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))

Crossrefs

Cf. A000384, A069099, A253714, A253716.

Sequence in context: A075702 A205629 A299796 * A205331 A154822 A061335

Adjacent sequences: A253712 A253713 A253714 * A253716 A253717 A253718

Keyword

nonn,easy

Author

Colin Barker, Jan 10 2015

Status

approved