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9-gonal numbers (A001106) that are the sum of two consecutive 9-gonal numbers.
4

%I #11 Mar 07 2016 06:12:41

%S 24486,959892121,37629690894906,1475159141502204841,

%T 57829188627539743273926,2267019851101653874322234161,

%U 88871712145057846553640480297546,3483948857243537849494160234302156081,136577763012789458630812222951472642381766

%N 9-gonal numbers (A001106) that are the sum of two consecutive 9-gonal numbers.

%H Colin Barker, <a href="/A258441/b258441.txt">Table of n, a(n) for n = 1..217</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (39203,-39203,1).

%F a(n) = 39203*a(n-1) - 39203*a(n-2) + a(n-3).

%F G.f.: -x*(x^2-32537*x+24486) / ((x-1)*(x^2-39202*x+1)).

%F a(n) = (46+(89-36*sqrt(2))*(19601+13860*sqrt(2))^(-n)+(89+36*sqrt(2))*(19601+13860*sqrt(2))^n)/224. - _Colin Barker_, Mar 07 2016

%e 24486 is in the sequence because A001106(84) = 24486 = 12036 + 12450 = A001106(59) + A001106(60), where A001106(k) is the k-th 9-gonal number.

%o (PARI) Vec(-x*(x^2-32537*x+24486)/((x-1)*(x^2-39202*x+1)) + O(x^20))

%Y Cf. A001106, A258442, A258443, A258444.

%K nonn,easy

%O 1,1

%A _Colin Barker_, May 30 2015