Search: id:A007584
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%I A007584 M4695
%S A007584 0,1,10,34,80,155,266,420,624,885,1210,1606,2080,2639,3290,
%T A007584 4040,4896,5865,6954,8170,9520,11011,12650,14444,16400,18525,
%U A007584 20826,23310,25984,28855,31930
%N A007584 9-gonal (or enneagonal) pyramidal numbers: n(n+1)(7n-4)/6.
%D A007584 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007584 A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, 
               p. 194.
%F A007584 a(n)= (7*n-4)*binomial(n+1, 2)/3. G.f.: x*(1+6*x)/(1-x)^4.
%p A007584 a:=n->sum((n+j)^2-(n+j), j=0..n): seq(a(n)/2, n=0..30); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), May 26 2008
%t A007584 f[n_]:=7*n+1; s1=s2=0;lst={};Do[a=f[n];s1+=a;s2+=s1;AppendTo[lst,s2],
               {n,0,6!}];lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Jun 
               25 2009]
%Y A007584 Cf. A093564 ((7, 1) Pascal, column m=3). Partial sums of A001106.
%Y A007584 Sequence in context: A002601 A020495 A008527 this_sequence A009924 A019257 
               A020877
%Y A007584 Adjacent sequences: A007581 A007582 A007583 this_sequence A007585 A007586 
               A007587
%K A007584 easy,nonn
%O A007584 0,3
%A A007584 N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy.

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