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Numbers n such that T(n) + T(n+1) + ... + T(n+21) is a square, where T(m) = A000217(m) is the m-th triangular number.
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%I #17 Jun 13 2015 00:55:23

%S 35,75,911,1707,18383,34263,366947,683751,7320755,13640955,146048351,

%T 272135547,2913646463,5429070183,58126881107,108309268311,

%U 1159623975875,2160756296235,23134352636591,43106816656587,461527428756143,859975576835703,9207414222486467

%N Numbers n such that T(n) + T(n+1) + ... + T(n+21) is a square, where T(m) = A000217(m) is the m-th triangular number.

%C Positive integers y in the solutions to 2*x^2-22*y^2-484*y-3542 = 0.

%H Colin Barker, <a href="/A254443/b254443.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,20,-20,-1,1).

%F G.f.: x*(9*x^4+4*x^3-136*x^2-40*x-35) / ((x-1)*(x^4-20*x^2+1)).

%o (PARI) Vec(x*(9*x^4+4*x^3-136*x^2-40*x-35)/((x-1)*(x^4-20*x^2+1)) + O(x^100))

%Y Cf. A176541, A176542, A000217, A000292, A001110, A077415.

%Y Cf. A116476 (length 11), A257293 (length 13).

%K nonn,easy

%O 1,1

%A _Colin Barker_, May 04 2015