Search: id:A008778
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%I A008778
%S A008778 1,5,13,26,45,71,105,148,201,265,341,430,533,651,785,936,
%T A008778 1105,1293,1501,1730,1981,2255,2553,2876,3225,3601,4005,
%U A008778 4438,4901,5395,5921,6480,7073,7701,8365,9066,9805,10583
%N A008778 Number of n-dimensional partitions of 4. Number of terms in 4th derivative 
               of a function composed with itself n times.
%C A008778 Let m(i,1)=i; m(1,j)=j; m(i,j)=m(i-1,j)-m(i-1,j-1); then a(n)=m(n+3,3) 
               - Benoit Cloitre (benoit7848c(AT)orange.fr), May 08 2002
%C A008778 a(n) = number of (n+6)-bit binary sequences with exactly 6 1's none of 
               which is isolated. - David Callan (callan(AT)stat.wisc.edu), Jul 
               15 2004
%C A008778 If a 2-set Y and 2-set Z, having one element in common, are subsets of 
               an n-set X then a(n-4) is the number of 4-subests of X intersecting 
               both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Oct 03 2007
%C A008778 A008778=Sum of first n Triangular numbers plus previous Triangular number. 
               [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Oct 13 2009]
%D A008778 G. E. Andrews, The Theory of Partitions, Add.-Wes. '76, p. 190.
%H A008778 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative 
               Functions</a>
%H A008778 P. Chinn and S. Heubach, <a href="http://www.cs.uwaterloo.ca/journals/
               JIS/index.html">Integer Sequences Related to Compositions without 
               2's</a>, J. Integer Seqs., Vol. 6, 2003.
%F A008778 a(n) = dot_product(n, n-1, ...2, 1)*(2, 3, ..., n, 1) for n = 2, 3, 4, 
               ... [ i.e. a(2) = (2, 1)*(2, 1), a(3) = (3, 2, 1)*(2, 3, 1). ] (Clark 
               Kimberling)
%F A008778 a(n) = (n+1)*(n^2+8n+6)/6 = a(n-1)+A034856(n+1) = A000297(n-1)+1 = A000217(n)+A000292(n+1) 
               = A000290(n-1)+A000292(n). - Henry Bottomley (se16(AT)btinternet.com), 
               Oct 25 2001
%F A008778 a(n) = Sum{0<=k, l<=n; k+l|n} k*l. - Ralf Stephan (ralf(AT)ark.in-berlin.de), 
               May 06 2005
%p A008778 1+4*k+4*binomial(k,2)+binomial(k,3);
%p A008778 with (combinat):a[0]:=0:for n from 1 to 50 do a[n]:=2*a[n-1]-a[n-2]+1 
               od: seq(a[n]+binomial(n+3,n), n=0..37); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Mar 17 2008
%t A008778 Clear[lst,n,a,f]; f[n_]:=n*(n+1)/2; a=0;lst={};Do[a+=f[n];AppendTo[lst,
               a+f[n-1]],{n,6!}];lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Oct 13 2009]
%Y A008778 Cf. A022811-A022817, A024207-A024210.
%Y A008778 Column 1 of triangle A094415.
%Y A008778 Cf. A002411, A008779.
%Y A008778 Sequence in context: A018394 A147451 A139595 this_sequence A014813 A160420 
               A147411
%Y A008778 Adjacent sequences: A008775 A008776 A008777 this_sequence A008779 A008780 
               A008781
%K A008778 nonn
%O A008778 0,2
%A A008778 N. J. A. Sloane (njas(AT)research.att.com).

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