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A262489 The index of the first of two consecutive positive triangular numbers (A000217) the sum of which is equal to the sum of three consecutive positive triangular numbers.

%I A262489 #6 Sep 27 2015 08:22:51
%S A262489 7,18,78,187,781,1860,7740,18421,76627,182358,758538,1805167,7508761,
%T A262489 17869320,74329080,176888041,735782047,1751011098,7283491398,
%U A262489 17333222947,72099131941,171581218380,713707828020,1698478960861,7064979148267,16813208390238
%N A262489 The index of the first of two consecutive positive triangular numbers (A000217) the sum of which is equal to the sum of three consecutive positive triangular numbers.
%C A262489 For the index of the first of the corresponding three consecutive triangular numbers, see A165517.
%H A262489 Colin Barker, <a href="/A262489/b262489.txt">Table of n, a(n) for n = 1..1000</a>
%H A262489 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,10,-10,-1,1).
%F A262489 a(n) = a(n-1)+10*a(n-2)-10*a(n-3)-a(n-4)+a(n-5) for n>5.
%F A262489 G.f.: -x*(x^4-x^3-10*x^2+11*x+7) / ((x-1)*(x^4-10*x^2+1)).
%e A262489 7 is in the sequence because T(7)+T(8) = 28+36 = 64 = 15+21+28 = T(5)+T(6)+T(7), where T(k) is the k-th triangular number.
%o A262489 (PARI) Vec(-x*(x^4-x^3-10*x^2+11*x+7)/((x-1)*(x^4-10*x^2+1)) + O(x^30))
%Y A262489 Cf. A000217, A165517, A262490, A262491, A262492.
%K A262489 nonn,easy
%O A262489 1,1
%A A262489 _Colin Barker_, Sep 24 2015