Search: id:A059845
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%I A059845
%S A059845 0,7,17,30,46,65,87,112,140,171,205,242,282,325,371,420,472,527,585,646,
%T A059845 710,777,847,920,996,1075,1157,1242,1330,1421,1515,1612,1712,1815,1921,
%U A059845 2030,2142,2257,2375,2496,2620,2747,2877,3010,3146,3285,3427,3572,3720
%N A059845 (n/2)*(3*n + 11).
%C A059845 Number of Euclidean spaces for every compact Riemannian n-manifold to 
               be realizable as a sub-manifold.
%D A059845 John Nash, The Imbedding Problem For Riemannian Manifolds, Annals of 
               Mathematics, Vol. 63, No. 1, 1956, pp. 20-63.
%H A059845 Harry J. Smith, <a href="b059845.txt">Table of n, a(n) for n=0,...,2000</
               a>
%F A059845 sum (n+j-1,j=4..n). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Sep 12 2006
%F A059845 a(n)=3*n+a(n-1)+1 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 08 2009]
%e A059845 For n=2, a(2)=3*2+0+1=7; n=3, a(3)=3*3+7+1=17; n=4, a(4)=3*4+17+1=30 
               [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]
%t A059845 s=0;lst={s};Do[s+=n++ +7;AppendTo[lst, s], {n, 0, 6!, 3}];lst [From Vladimir 
               Orlovsky (4vladimir(AT)gmail.com), Nov 16 2008]
%t A059845 Table[Sum[i + n - 3, {i, 5, n}], {n, 4, 52}] [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jul 11 2009]
%o A059845 (PARI) { for (n=0, 2000, write("b059845.txt", n, " ", n*(3*n + 11)/2); 
               ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 29 2009]
%Y A059845 The generalized pentagonal numbers b*n+3*n*(n-1)/2, for b = 1 through 
               12, form sequences A000326, A005449, A045943, A115067, A140090, A140091, 
               A059845, A140672, A140673, A140674, A140675, A151542.
%Y A059845 Sequence in context: A045575 A029532 A088566 this_sequence A006142 A001123 
               A094080
%Y A059845 Adjacent sequences: A059842 A059843 A059844 this_sequence A059846 A059847 
               A059848
%K A059845 easy,nonn,new
%O A059845 0,2
%A A059845 Jason Earls (zevi_35711(AT)yahoo.com), Mar 10 2001

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