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A253716 Hexagonal numbers (A000384) which are also centered heptagonal numbers (A069099). 3


%S 1,16322041,4145734153,67933251842771953,17254778510170993681,

%T 282742011610770921096804841,71815357774355276244995175961,

%U 1176788140728629029198108610250463201,298899554649081431834808455098428958753,4897858370145334123819452782766901335994312153

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

%H Colin Barker, <a href="/A253716/b253716.txt">Table of n, a(n) for n = 1..208</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,4162056194,0,-1).

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

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

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

%t LinearRecurrence[{0,4162056194,0,-1},{1,16322041,4145734153,67933251842771953},20] (* _Harvey P. Dale_, Jan 05 2017 *)

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

%Y Cf. A000384, A069099, A253714, A253715.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jan 10 2015

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Last modified April 18 15:54 EDT 2021. Contains 343089 sequences. (Running on oeis4.)