Search: id:A156572
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%I A156572
%S A156572 289,529,1369,4225,13225,42025,139129,444889,1423249,4721929,15108769,
%T A156572 48344209,160402225,513249025,1642275625,5448949489,17435353849,
%U A156572 55789022809,185103876169,592288777609,1895184495649,6288082836025
%N A156572 Squares of the form k^2+(k+23)^2 with integer k.
%C A156572 Square roots of k^2+(k+17)^2 are in A156567, values k are in A118337.
%C A156572 lim_{n -> infinity} a(n)/a(n-3) = 17+12*sqrt(2).
%C A156572 lim_{n -> infinity} a(n)/a(n-1) = ((627+238*sqrt(2))/23^2)^2 for n mod 
               3 = 1.
%C A156572 lim_{n -> infinity} a(n)/a(n-1) = ((27+10*sqrt(2))/23)^2 for n mod 3 
               = {0, 2}.
%F A156572 a(n) = 34*a(n-3)-a(n-6)-4232 for n > 6; a(1)=289, a(2)=529, a(3)=1369, 
               a(4)=4225, a(5)=13225, a(6)=42025.
%F A156572 G.f.: x*(289+240*x+840*x^2-6970*x^3+840*x^4+240*x^5+289*x^6)/((1-x)*(1-34*x^3+x^6)).
%e A156572 4225 = 65^2 is of the form k^2+(k+23)^2 with k = 33: 33^2+56^2 = 4225. 
               Hence 4225 is in the sequence.
%o A156572 (PARI) {forstep(n=-8, 1800000, [1, 3], if(issquare(a=2*n*(n+23)+529), 
               print1(a, ",")))}
%Y A156572 Equals A156567^2. Cf. A156575 (first trisection), A156573 (second trisection), 
               A156574 (third trisection).
%Y A156572 Cf. A118337, A156035 (decimal expansion of 3+2*sqrt(2)), A156164 (decimal 
               expansion of 17+12*sqrt(2)), A156571 (decimal expansion of (27+10*sqrt(2))/
               23), A157472 (decimal expansion of (627+238*sqrt(2))/23^2).
%Y A156572 Sequence in context: A107739 A008367 A152852 this_sequence A157990 A112077 
               A152934
%Y A156572 Adjacent sequences: A156569 A156570 A156571 this_sequence A156573 A156574 
               A156575
%K A156572 nonn
%O A156572 1,1
%A A156572 Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 11 2009
%E A156572 Revised by Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Feb 16 2009
%E A156572 G.f. corrected, third comment and cross-references edited by Klaus Brockhaus 
               (klaus-brockhaus(AT)t-online.de), Sep 22 2009

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