Search: id:A007586
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%I A007586 M4835
%S A007586 0,1,12,42,100,195,336,532,792,1125,1540,2046,2652,3367,4200,
%T A007586 5160,6256,7497,8892,10450,12180,14091,16192,18492,21000,
%U A007586 23725,26676,29862,33292,36975,40920,45136,49632,54417,59500
%N A007586 11-gonal (or hendecagonal) pyramidal numbers: n(n+1)(3n-2)/2.
%D A007586 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007586 A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, 
               p. 194.
%F A007586 G.f.: x*(1+8*x)/(1-x)^4.
%F A007586 Starting with 1 equals binomial transform of [1, 11, 19, 9, 0, 0, 0,...]. 
               - Gary W. Adamson (qntmpkt(AT)yahoo.com), Nov 02 2007
%p A007586 restart: a:=n->sum(sum(k, j=3..n), k=0..n): seq(a(n), n=1..53):b:=n->
               sum(sum(n, j=1..n), k=0..n): seq(a(n), n=1..53):c:=b+a:seq(c(n), 
               n=0..35); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 
               24 2008]
%p A007586 a:=n->add(binomial(n,2)+add(n, j=3..n),j=2..n):seq(a(n), n=1..40); [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Aug 27 2008]
%Y A007586 Cf. A051682.
%Y A007586 Cf. A093644 ((9, 1) Pascal, column m=3).
%Y A007586 Sequence in context: A005901 A090554 A009948 this_sequence A122973 A074356 
               A088826
%Y A007586 Adjacent sequences: A007583 A007584 A007585 this_sequence A007587 A007588 
               A007589
%K A007586 nonn,easy,nice
%O A007586 0,3
%A A007586 N. J. A. Sloane (njas(AT)research.att.com), R. K. Guy.

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