Search: id:A036428
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%I A036428
%S A036428 1,225,43681,8473921,1643897025,318907548961,61866420601441,
%T A036428 12001766689130625,2328280871270739841,451674487259834398561,
%U A036428 87622522247536602581025,16998317641534841066320321
%N A036428 Square octagonal numbers.
%C A036428 Also, numbers simultaneously octagonal and centered octagonal. - Steven 
               Schlicker (schlicks(AT)gvsu.edu), Apr 24 2007
%D A036428 S. Schlicker, Numbers Simultaneously Polygonal and Centered Polygonal, 
               submitted.
%H A036428 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               OctagonalSquareNumber.html">Link to a section of The World of Mathematics.</
               a>
%F A036428 Let x(n) + y(n)*sqrt(48) = (8+sqrt(48))*(7+sqrt(48))^n, s(n) = (y(n)+1)/
               2; then a(n) = (1/2)*(2+8*(s(n)^2-s(n))) - Steven Schlicker (schlicks(AT)gvsu.edu), 
               Apr 24 2007
%F A036428 a(n+2)=194*a(n+1)-a(n)+32 and also a(n+1)=97*a(n)+56*(3*a(n)^2+a(n))^0.5. 
               - Richard Choulet, Sep 26 2007
%F A036428 G.f.: x(x^2+30x+1)/[(1-x)(1-194x+x^2)].
%F A036428 a(n)=-(1/6)+(7/12)*{[97-56*sqrt(3)]^n+[97+56*sqrt(3)]^n}-(1/3)*sqrt(3)*{[97-56*sqrt(3)]^n 
               -[97+56*sqrt(3)]^n}, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), 
               Nov 25 2008]
%p A036428 CP := n -> 1+1/2*8*(n^2-n): N:=10: u:=7: v:=1: x:=8: y:=1: k_pcp:=[1]: 
               for i from 1 to N do tempx:=x; tempy:=y; x:=tempx*u+48*tempy*v: y:=tempx*v+tempy*u: 
               s:=(y+1)/2: k_pcp:=[op(k_pcp),CP(s)]: end do: k_pcp; - Steven Schlicker 
               (schlicks(AT)gvsu.edu), Apr 24 2007
%Y A036428 Cf. A000567, A016754.
%Y A036428 Cf. A006060, A006051, A028230, A046184.
%Y A036428 Sequence in context: A151651 A051364 A061051 this_sequence A109688 A013757 
               A151653
%Y A036428 Adjacent sequences: A036425 A036426 A036427 this_sequence A036429 A036430 
               A036431
%K A036428 nonn,easy
%O A036428 1,2
%A A036428 Jean-Francois Chariot (jean-francois.chariot(AT)afoc.alcatel.fr)
%E A036428 More terms from Eric Weisstein (eric(AT)weisstein.com)
%E A036428 Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 02 2007

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