A253715 -id:A253715 - 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)).

A253716 Hexagonal numbers (A000384) which are also centered heptagonal numbers (A069099).

Original entry on oeis.org

1, 16322041, 4145734153, 67933251842771953, 17254778510170993681, 282742011610770921096804841, 71815357774355276244995175961, 1176788140728629029198108610250463201, 298899554649081431834808455098428958753, 4897858370145334123819452782766901335994312153

Offset: 1

Colin Barker, Jan 10 2015

			16322041 is in the sequence because it is the 2857th hexagonal number and the 2160th centered heptagonal number.

Colin Barker, Table of n, a(n) for n = 1..208
Index entries for linear recurrences with constant coefficients, signature (0,4162056194,0,-1).

Cf. A000384, A069099, A253714, A253715.

LinearRecurrence[{0,4162056194,0,-1},{1,16322041,4145734153,67933251842771953},20] (* Harvey P. Dale, Jan 05 2017 *)

Vec(-x*(x-1)*(x^2+16322042*x+1)/((x^2-64514*x+1)*(x^2+64514*x+1)) + O(x^100))

a(n) = 4162056194*a(n-2)-a(n-4).

G.f.: -x*(x-1)*(x^2+16322042*x+1) / ((x^2-64514*x+1)*(x^2+64514*x+1)).

cp's OEIS Frontend

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

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