A253716 -id:A253716 - cp's OEIS frontend

A253714 Indices of hexagonal numbers (A000384) which are also centered heptagonal numbers (A069099).

1, 2857, 45529, 184300369, 2937241777, 11889953986681, 189493215939721, 767068491312421537, 12224965330197902689, 49486656636639609035209, 788681413122894278122297, 3192582165489099245985035761, 50880992673985436128583949841

Offset: 1

Colin Barker, Jan 10 2015

Also positive integers x in the solutions to 4*x^2-7*y^2-2*x+7*y-2 = 0, the corresponding values of y being A253715.

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

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).

Cf. A000384, A069099, A253715, A253716.

Vec(-x*(x^4+2856*x^3-21842*x^2+2856*x+1)/((x-1)*(x^2-254*x+1)*(x^2+254*x+1)) + O(x^100))

a(n) = a(n-1)+64514*a(n-2)-64514*a(n-3)-a(n-4)+a(n-5).

G.f.: -x*(x^4+2856*x^3-21842*x^2+2856*x+1) / ((x-1)*(x^2-254*x+1)*(x^2+254*x+1)).

A253715 Indices of centered heptagonal numbers (A069099) which are also hexagonal numbers (A000384).

Original entry on oeis.org

1, 2160, 34417, 139317984, 2220346081, 8987960385360, 143243407002961, 579849276161764800, 9241205157168647617, 37408396193312133889584, 596187109366334725327921, 2413365271435489729590825120, 38462415164418513312636815521, 155695847083980788221510357869840

Offset: 1

Colin Barker, Jan 10 2015

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.

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

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).

Cf. A000384, A069099, A253714, A253716.

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

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))

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)).

cp's OEIS Frontend

A253714 Indices of hexagonal numbers (A000384) which are also centered heptagonal numbers (A069099).

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