A261995 - OEIS

%I #6 Sep 08 2015 08:54:00

%S 42,123,315,1827,4659,13650,34794,201114,512610,1501539,3827187,

%T 22120875,56382603,165155802,420955938,2433095298,6201573882,

%U 18165636843,46301326155,267618362067,682116744579,1998054897090,5092724921274,29435586732234,75026640329970

%N The first of four consecutive positive integers the sum of the squares of which is equal to the sum of the squares of twenty-one consecutive positive integers.

%C For the first of the corresponding twenty-one consecutive positive integers, see A261996.

%H Colin Barker, <a href="/A261995/b261995.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,110,-110,0,0,-1,1).

%F G.f.: -3*x*(6*x^8+8*x^6+27*x^5-596*x^4+504*x^3+64*x^2+27*x+14) / ((x-1)*(x^8-110*x^4+1)).

%e 42 is in the sequence because 42^2 + ... + 45^2 = 7574 = 8^2 + ... + 28^2.

%o (PARI) Vec(-3*x*(6*x^8+8*x^6+27*x^5-596*x^4+504*x^3+64*x^2+27*x+14)/((x-1)*(x^8-110*x^4+1)) + O(x^40))

%Y Cf. A157092, A246642, A261996.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Sep 08 2015