Search: id:A101097
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%I A101097
%S A101097 1,12,69,272,846,2232,5214,11088,21879,40612,71643,121056,197132,310896,
%T A101097 476748,713184,1043613,1497276,2110273,2926704,3999930,5393960,7184970,
%U A101097 9462960,12333555,15919956,20365047,25833664,32515032,40625376,50410712
%N A101097 Fourth partial sums of cubes (A000578).
%H A101097 C. Rossiter, <a href="http://noticingnumbers.net/300SeriesCube.htm">Depictions, 
               Explorations and Formulas of the Euler/Pascal Cube</a>.
%F A101097 a(n) = {(n*(1 + n)*(2 + n)*(3 + n)*(4 + n)*(2 + n*(4 + n)))/840}.
%F A101097 This sequence could be obtained from the general formula a(n)=n*(n+1)*(n+2)*(n+3)* 
               ...* (n+k) *(n*(n+k) + (k-1)*k/6)/((k+3)!/6) at k=4 - Alexander R. 
               Povolotsky (pevnev(AT)juno.com), May 17 2008
%F A101097 O.g.f.: x(1+4x+x^2)/(1-x)^(k+4), k=4. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Jun 13 2008
%t A101097 s1=s2=s3=s4=0; lst={}; Do[s1+=n^3; s2+=s1; s3+=s2; s4+=s3; AppendTo[lst,
               s4],{n,0,6!}]; lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Jan 15 2009]
%o A101097 (PARI) a(n)=sum(s=1,n,sum(l=1,s,sum(j=1,l, sum(m=1, j, sum(i=m*(m+1)/
               2-m+1, m*(m+1)/2, (2*i-1)))))) - Alexander R. Povolotsky (pevnev(AT)juno.com), 
               May 17 2008
%Y A101097 Cf. A101102, A101094.
%Y A101097 Cf. A101102, A101094, A024166, A000537.
%Y A101097 Cf. A024166, A101094 [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Jan 15 2009]
%Y A101097 Sequence in context: A059585 A050484 A096425 this_sequence A067702 A163193 
               A088832
%Y A101097 Adjacent sequences: A101094 A101095 A101096 this_sequence A101098 A101099 
               A101100
%K A101097 easy,nonn
%O A101097 1,2
%A A101097 Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 15 2004
%E A101097 Edited by Ralf Stephan, Dec 16 2004

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