Search: id:A059722
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%I A059722
%S A059722 0,1,10,39,100,205,366,595,904,1305,1810,2431,3180,4069,5110,6315,7696,
%T A059722 9265,11034,13015,15220,17661,20350,23299,26520,30025,33826,37935,42364,
%U A059722 47125,52230,57691,63520,69729,76330,83335,90756,98605,106894,115635,124840
%N A059722 a(n) = n*(2*n^2 - 2*n + 1).
%C A059722 Mean of first four nonnegative powers of 2n+1, i.e. ((2n+1)^0+(2n+1)^1+(2n+1)^2+(2n+1)^3)/
               4. E.g. a(2)=(1+3+9+27)/4=10
%C A059722 Equatorial structured meta-diamond numbers, the n-th number from an equatorial 
               structured n-gonal diamond number sequence. There are no 1- or 2-gonal 
               diamonds, so 1 and (n+2) are used as the first and second terms since 
               all the sequences begin as such. - James A. Record (james.record(AT)gmail.com). 
               Nov 07, 2004
%C A059722 Starting with offset 1 = row sums of triangle A143803. [From Gary W. 
               Adamson (qntmpkt(AT)yahoo.com), Sep 01 2008]
%H A059722 Harry J. Smith, <a href="b059722.txt">Table of n, a(n) for n=0,...,1000</
               a>
%F A059722 a(n) = A053698(2n+1)/4
%F A059722 a(n) = sum (((n+j-1)^2-j^2+1),j=1..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Sep 13 2006
%F A059722 G.f.: x(1+x)(1+5x)/(1-x)^4. a(n)= A002414(n-1)+A002414(n). a(n+1)-a(n)=A136392(n+1). 
               [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 02 2008]
%o A059722 (PARI) { for (n=0, 1000, write("b059722.txt", n, " ", n*(2*n^2 - 2*n 
               + 1)); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 
               28 2009]
%Y A059722 Cf. A000330, A005900, A081436, A100178, A100179, A059722: "equatorial" 
               structured diamonds; A000447: "polar" structured meta-diamond; A006484 
               for other structured meta numbers; and A100145 for more on structured 
               numbers.: James A. Record (james.record(AT)gmail.com). Nov 07, 2004
%Y A059722 Cf. A059721, A059723.
%Y A059722 Cf. A143803 [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 01 2008]
%Y A059722 Sequence in context: A050479 A156674 A022277 this_sequence A074225 A055514 
               A055233
%Y A059722 Adjacent sequences: A059719 A059720 A059721 this_sequence A059723 A059724 
               A059725
%K A059722 nonn
%O A059722 0,3
%A A059722 Henry Bottomley (se16(AT)btinternet.com), Feb 07 2001
%E A059722 Edited with new definition by N. J. A. Sloane (njas(AT)research.att.com), 
               Aug 29 2008

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