Search: id:A007667
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%I A007667 M4037
%S A007667 5,365,35645,3492725,342251285,33537133085,3286296790925,
%T A007667 322023548377445,31555021444198565,3092070077983081805,
%U A007667 302991312620897818205,29690056566770003102165
%N A007667 The sum of both two and three consecutive squares.
%C A007667 a(n) = (b(n)-1)^2+b(n)^2+(b(n)+1)^2 = c(n)^2+(c(n)+1)^2, where b(n) is 
               A054320 and c(n) is A031138; a(n) = 3b(n)+2, where b(n) is a Star 
               square number (A006061).
%D A007667 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007667 M. Gardner, Time Travel and Other Mathematical Bewilderments. Freeman, 
               NY, 1988, p. 22.
%H A007667 <a href="Sindx_Su.html#ssq">Index entries for sequences related to sums 
               of squares</a>
%F A007667 A007667 = 3*Square star numbers (A006061) + 2.
%F A007667 a(n) = 99(a(n-1) - a(n-2))+a(n-3); a(n)=3(5 - 2sqrt(6))/8*(sqrt(3) + 
               sqrt(2))^(4n) + 3*(5 + 2sqrt(6))/8*(sqrt(3) - sqrt(2))^(4n) + 5/4
%e A007667 a(2) = 365 = 13^2+14^2 = 10^2+11^2+12^2.
%Y A007667 Cf. A003154, A031138, A006061, A054320.
%Y A007667 Sequence in context: A006108 A061456 A006430 this_sequence A121668 A160193 
               A098038
%Y A007667 Adjacent sequences: A007664 A007665 A007666 this_sequence A007668 A007669 
               A007670
%K A007667 nonn
%O A007667 1,1
%A A007667 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
%E A007667 Additional comments from Ignacio Larrosa Canestro (ignacio.larrosa(AT)eresmas.net) 
               Feb 27 2000
%E A007667 Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006

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