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%I #24 Jun 13 2015 00:54:08
%S 5,39,237,1391,8117,47319,275805,1607519,9369317,54608391,318281037,
%T 1855077839,10812186005,63018038199,367296043197,2140758220991,
%U 12477253282757,72722761475559,423859315570605,2470433131948079
%N Indices of the smallest of four consecutive triangular numbers summing up to a square.
%C Positive integers n such that A000217(n) + A000217(n + 1) + A000217(n + 2) + A000217(n + 3) is a square (=A075870(n+1)^2).
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (7,-7,1).
%F a(n) = A002315(n) - 2.
%F G.f. x*(1+x)*(x-5) / ( (x-1)*(1-6*x+x^2) ). - _R. J. Mathar_, Dec 19 2011
%F a(n+2) = 6*a(n+1) - a(n) + 8; a(n+3) = 7*a(n+2) - 7*a(n+1) + a(n); a(n+1) = (-4 + (7 + 5*r)*(3 + 2*r)^n + (7 - 5*r)*(3 - 2*r)^n)/2 where r = sqrt(2). - _Paul Weisenhorn_, Jan 13 2013
%Y Cf. A176541, A176542, A165517, A116476, A075870
%K nonn
%O 1,1
%A _Max Alekseyev_, Dec 18 2011
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