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A262492 The index of the first of two consecutive positive triangular numbers (A000217) the sum of which is equal to the sum of thirteen consecutive positive triangular numbers.

%I A262492 #6 Sep 27 2015 08:17:48
%S A262492 25,90,207,1117,2560,9255,21202,114022,261195,944020,2162497,11629227,
%T A262492 26639430,96280885,220553592,1186067232,2716960765,9819706350,
%U A262492 22494303987,120967228537,277103358700,1001513766915,2294198453182,12337471243642,28261825626735
%N A262492 The index of the first of two consecutive positive triangular numbers (A000217) the sum of which is equal to the sum of thirteen consecutive positive triangular numbers.
%C A262492 For the index of the first of the corresponding thirteen consecutive triangular numbers, see A257293.
%H A262492 Colin Barker, <a href="/A262492/b262492.txt">Table of n, a(n) for n = 1..1000</a>
%H A262492 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,102,-102,0,0,-1,1).
%F A262492 G.f.: -x*(12*x^8+13*x^6+65*x^5-1107*x^4+910*x^3+117*x^2+65*x+25) / ((x-1)*(x^4-10*x^2-1)*(x^4+10*x^2-1)).
%e A262492 25 is in the sequence because T(25)+T(26) = 325+351 = 676 = 6+...+120 = T(3)+...+T(15), where T(k) is the k-th triangular number.
%o A262492 (PARI) Vec(-x*(12*x^8+13*x^6+65*x^5-1107*x^4+910*x^3+117*x^2+65*x+25)/((x-1)*(x^4-10*x^2-1)*(x^4+10*x^2-1)) + O(x^30))
%Y A262492 Cf. A000217, A257293, A262489, A262490, A262491.
%K A262492 nonn,easy
%O A262492 1,1
%A A262492 _Colin Barker_, Sep 24 2015