Search: id:A028552
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%I A028552
%S A028552 0,4,10,18,28,40,54,70,88,108,130,154,180,208,238,270,304,340,378,
%T A028552 418,460,504,550,598,648,700,754,810,868,928,990,1054,1120,1188,
%U A028552 1258,1330,1404,1480,1558,1638,1720,1804,1890,1978,2068
%N A028552 n(n+3).
%C A028552 n(n-3) (n >= 3) is the number of [body] diagonals of an n-gonal prism 
               - Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr).
%C A028552 a(n) = A028387(n)-1. Half of the difference between n(n+1)(n+2)(n+3) 
               and the largest square less than it. Calling this difference "SquareMod": 
               a(n) = (1/2)*SqareMod(n(n+1)(n+2)(n+3)). - Rainer Rosenthal (r.rosenthal(AT)web.de), 
               Sep 04 2004
%C A028552 n != -2 such that x^4 + x^3 - n*x^2 + x + 1 is reducible over the integers. 
               Starting at 10: n such that x^4 + x^3 - n*x^2 + x + 1 is a product 
               of irreducible quadratic factors over the integers. - James Buddenhagen 
               (jbuddenh(AT)gmail.com), Apr 19 2005
%C A028552 If a 3-set Y and a 3-set Z, having two element in common, are subsets 
               of an n-set X then a(n-4) is the number of 3-subests of X intersecting 
               both Y and Z. - Milan R. Janjic (agnus(AT)blic.net), Oct 03 2007
%C A028552 Starting with offset 1 = binomial transform of [4, 6, 2, 0, 0, 0,...] 
               [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Jan 09 2009]
%C A028552 a(A002522(n)) = A156798(n). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Feb 16 2009]
%C A028552 Except for the first term, a(n)=2*n+a(n-1)+2 (with a(1)=4) [From Vincenzo 
               Librandi (vincenzo.librandi(AT)tin.it), Nov 07 2009]
%H A028552 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative 
               Functions</a>
%H A028552 P. De Geest, <a href="http://www.worldofnumbers.com/consemor.htm">Palindromic 
               Quasipronics of the form n(n+x)</a>
%p A028552 a:=n->sum(binomial(n,1),j=4..n): seq(a(n), n=3..47); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Feb 12 2007
%p A028552 a:=n->sum(sum(3, j=3..n)/3, k=0..n): seq(a(n), n=2..46); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), May 30 2007
%p A028552 with (combinat):seq(fibonacci(3, n)+n-3, n=1..45); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jun 07 2008
%p A028552 a:=n->sum(1+sum(1, k=5..n),k=1..n):seq(a(n), n=4...47); - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jun 11 2008
%p A028552 with(finance):seq(add(cashflows([k, k, 2], 0 ), k=1..n), n=0..45); # 
               [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]
%t A028552 lst={};Do[AppendTo[lst, n*(n+3)], {n, 0, 6!, 1}];lst [From Vladimir Orlovsky 
               (4vladimir(AT)gmail.com), Nov 07 2008]
%Y A028552 Cf. A028387, A062145.
%Y A028552 Cf. A002522.
%Y A028552 Sequence in context: A009876 A161958 A013921 this_sequence A009877 A009880 
               A025712
%Y A028552 Adjacent sequences: A028549 A028550 A028551 this_sequence A028553 A028554 
               A028555
%K A028552 nonn,easy,nice,new
%O A028552 0,2
%A A028552 Patrick De Geest (pdg(AT)worldofnumbers.com)

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