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%I #20 Jul 31 2015 18:11:20
%S 1,3,7,71,199,455,4551,12743,29127,291271,815559,1864135,18641351,
%T 52195783,119304647,1193046471,3340530119,7635497415,76354974151,
%U 213793927623,488671834567,4886718345671,13682811367879,31274997412295
%N a(n) = a(n-1) + 2^A047240(n) for n>1, a(1)=1.
%H Vincenzo Librandi, <a href="/A113841/b113841.txt">Table of n, a(n) for n = 1..300</a>
%H Vladimir Pletser, <a href="http://arxiv.org/abs/1409.7969">Congruence conditions on the number of terms in sums of consecutive squared integers equal to squared integers</a>, arXiv:1409.7969 [math.NT], 2014.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 64, -64).
%F G.f.: x*(1+2*x+4*x^2)/((-1+x)*(-1+4*x)*(1+4*x+16*x^2)). - _Vaclav Kotesovec_, Nov 28 2012
%F a(1)=1, a(2)=3, a(3)=7, a(4)=71, a(n)=a(n-1)+64*a(n-3)-64*a(n-4). - _Harvey P. Dale_, Nov 18 2013
%t CoefficientList[Series[(1 + 2 x + 4 x^2) / ((-1 + x) (-1 + 4 x) (1 + 4 x + 16 x^2)), {x, 0, 30}], x] (* _Vincenzo Librandi_, May 19 2013 *)
%t LinearRecurrence[{1,0,64,-64},{1,3,7,71},30] (* _Harvey P. Dale_, Nov 18 2013 *)
%Y Cf. A099974, A112627, A080355, A080567, A099969, A099970, A099971.
%K nonn,easy
%O 1,2
%A _Artur Jasinski_, Jan 27 2006
%E Edited with better definition and offset corrected by _Omar E. Pol_, Jan 08 2009
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