%I
%S 1,15,1075,21201,1549717,30571395,2234690407,44083929957,
%T 3222422016745,63568996426167,4646730313455451,91666448762602425,
%U 6700581889580743165,132182955546676270251,9662234438045118188047,190607730231858419099085,13932935359079170846420177
%N Indices of heptagonal numbers that are also decagonal.
%C As n increases, the ratios of consecutive terms settle into an approximate 2cycle with a(n)/a(n1) bounded above and below by 1/9*(329+104*sqrt(10)) and 1/9*(89+28*sqrt(10)) respectively.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,1442,1442,1,1).
%F G.f.: x*(1+14*x382*x^262*x^33*x^4) / ((1x)*(138*x+x^2)*(1+38*x+x^2)).
%F a(n) = 1442*a(n2)a(n4)432.
%F a(n) = a(n1)+1442*a(n2)1442*a(n3)a(n4)+a(n5).
%F a(n) = 1/40*(((1)^nsqrt(10))*(2sqrt(10))*(3+sqrt(10))^(2*n1)+((1)^n+sqrt(10))*(2+sqrt(10))*(3sqrt(10))^(2*n1)+12).
%F a(n) = ceiling(1/40*((1)^nsqrt(10))*(2sqrt(10))*(3+sqrt(10))^(2*n1)).
%e The second heptagonal number that is also decagonal is A000566(15)=540. Hence a(2)=15.
%t LinearRecurrence[{1, 1442, 1442, 1, 1}, {1, 15, 1075, 21201, 1549717}, 17]
%Y Cf. A203408, A203410, A001107, A000566.
%K nonn,easy
%O 1,2
%A _Ant King_, Jan 02 2012
