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A253715 Indices of centered heptagonal numbers (A069099) which are also hexagonal numbers (A000384). 3
1, 2160, 34417, 139317984, 2220346081, 8987960385360, 143243407002961, 579849276161764800, 9241205157168647617, 37408396193312133889584, 596187109366334725327921, 2413365271435489729590825120, 38462415164418513312636815521, 155695847083980788221510357869840 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 21 10:28 EDT 2021. Contains 343149 sequences. (Running on oeis4.)