A253121 - OEIS

%I #9 Sep 04 2025 18:32:01

%S 18,1730,169498,16609050,1627517378,159480093970,15627421691658,

%T 1531327845688490,150054501455780338,14703809814820784610,

%U 1440823307350981111418,141185980310581328134330,13834785247129619176052898,1355667768238392097925049650

%N Numbers k such that the hexagonal number H(k) is equal to the sum of the octagonal numbers O(m), O(m+1), O(m+2) and O(m+3) for some m.

%C Also positive integers y in the solutions to 24*x^2-4*y^2+56*x+2*y+60 = 0, the corresponding values of x being A253120.

%H Colin Barker, <a href="/A253121/b253121.txt">Table of n, a(n) for n = 1..500</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (99,-99,1).

%F a(n) = 99*a(n-1)-99*a(n-2)+a(n-3).

%F G.f.: -2*x*(5*x^2-26*x+9) / ((x-1)*(x^2-98*x+1)).

%e 18 is in the sequence because H(18) = 630 = 96+133+176+225 = O(6)+O(7)+O(8)+O(9).

%o (PARI) Vec(-2*x*(5*x^2-26*x+9)/((x-1)*(x^2-98*x+1)) + O(x^100))

%Y Cf. A000384, A000567, A253120.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Dec 27 2014