Search: id:A069894
Results 1-1 of 1 results found.

%I A069894
%S A069894 2,10,26,50,82,122,170,226,290,362,442,530,626,730,842,962,1090,1226,
%T A069894 1370,1522,1682,1850,2026,2210,2402,2602,2810,3026,3250,3482,3722,3970,
%U A069894 4226,4490,4762,5042,5330,5626,5930,6242,6562,6890,7226,7570,7922,8282
%N A069894 Centered square numbers: 4*n^2 + 4*n + 2.
%C A069894 Any number may be substituted for y to yield similar sequences. The number 
               set used determines values given (i.e.- integer yields integer). 
               All centered square integers in the set of integers may be found 
               by this formula.
%C A069894 1/2 + 1/10 + 1/26 +...= (Pi/4)*tanh(Pi/2) [Jolley] - Gary W. Adamson 
               (qntmpkt(AT)yahoo.com), Dec 21 2006
%C A069894 Except for the first term, a(n)=8*n+a(n-1), (with a(1)=10) [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Oct 24 2009]
%D A069894 L. B. W. Jolley, "Summation of Series", Dover Publications, 1961, p. 
               176.
%F A069894 [y(2x + 1)]^2 + [y(2x^2 + 2x)]^2 = [y(2x^2 + 2x +1)]^2 where y = 2. If 
               a^2 + b^2 = c^2, then c^2 = y^2(4x^4 + 8x^3 + 8x^2 + 4x + 1). Also 
               2*A001844.
%F A069894 a(n) = (2n+1)^2+1. [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Nov 10 2008, corrected R. J. Mathar, Sep 16 2009]
%F A069894 a(n)=8*n+a(n-1)-8 (with a(1)=2) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 17 2009]
%e A069894 If y = 3, then 81 + 144 = 225; if y = 4, then 12^2 + 16^2 = 20^2; 7^2 
               + 24^2 = 25^2 = 15^2 + 20^2.
%e A069894 For n=2, a(2)=8*2+2-8=10; n=3, a(3)=8*3+10-8=26; n=4, a(4)=8*4+26-8=50 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 17 2009]
%t A069894 Table[4n(n + 1) + 2, {n, 0, 45}]
%t A069894 lst={};Do[AppendTo[lst, n^2+1], {n, 1, 2*4!, 2}];lst [From Vladimir Orlovsky 
               (4vladimir(AT)gmail.com), Nov 10 2008]
%Y A069894 Cf. A001844.
%Y A069894 Sequence in context: A058373 A167386 A027719 this_sequence A045605 A009307 
               A131130
%Y A069894 Adjacent sequences: A069891 A069892 A069893 this_sequence A069895 A069896 
               A069897
%K A069894 nonn,new
%O A069894 2,1
%A A069894 Glenn B. Cox (igloos_r_us(AT)canada.com), Apr 10 2002
%E A069894 Edited by Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 11 2002
%E A069894 Edited the equation 4n^2+4n+2=n^2+1 - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Sep 16 2009

Search completed in 0.001 seconds