%I #11 Aug 13 2018 16:37:42

%S 1,10,46,1045,5005,114886,550450,12636361,60544441,1389884770,

%T 6659338006,152874688285,732466636165,16814825826526,80564670640090,

%U 1849477966229521,8861381303773681,203425761459420730,974671378744464766,22374984282570050725

%N Indices of centered heptagonal numbers (A069099) which are also centered triangular numbers (A005448).

%C Also positive integers y in the solutions to 3*x^2 - 7*y^2 - 3*x + 7*y = 0, the corresponding values of x being A253476.

%H Colin Barker, <a href="/A253477/b253477.txt">Table of n, a(n) for n = 1..980</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,110,-110,-1,1).

%F a(n) = a(n-1)+110*a(n-2)-110*a(n-3)-a(n-4)+a(n-5).

%F G.f.: -x*(x^4+9*x^3-74*x^2+9*x+1) / ((x-1)*(x^4-110*x^2+1)).

%e 10 is in the sequence because the 10th centered heptagonal number is 316, which is also the 15th centered triangular number.

%t LinearRecurrence[{1,110,-110,-1,1},{1,10,46,1045,5005},30] (* _Harvey P. Dale_, Aug 13 2018 *)

%o (PARI) Vec(-x*(x^4+9*x^3-74*x^2+9*x+1)/((x-1)*(x^4-110*x^2+1)) + O(x^100))

%Y Cf. A005448, A069099, A253476, A253689.

%K nonn,easy

%O 1,2

%A _Colin Barker_, Jan 02 2015