Search: id:A145920
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%I A145920
%S A145920 0,1,5,35,70,210,330,715,1001,1820,2380,3876,4845,7315,8855,12650,14950,
%T A145920 20475,23751,31465,35960,46376,52360,66045,73815,91390,101270,123410,
%U A145920 135751,163185,178365,211876,230300,270725,292825,341055,367290,424270
%N A145920 List of numbers that are both pentagonal (A000326) and binomial coefficients 
               C (n, 4) (A000332).
%C A145920 All binomial cofficients C (n, 4) belong to the generalized pentagonal 
               sequence (A001318).
%H A145920 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PentagonalNumber.html">Pentagonal Number</a>.
%H A145920 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PentatopeNumber.html">Pentatope Number</a>.
%F A145920 a(n+1) = A000326 (A001318(n)).
%F A145920 Positive values of A000332(n) belong to the sequence if and only if 3 
               does not divide n. A000332(n) is positive when n>3.
%F A145920 Conjecture: a(n)=a(n-1)+4a(n-2)-4a(n-3)-6a(n-4)+6a(n-5)+4a(n-6)-4a(n-7)-a(n-8)+a(n-9). 
               Conjecture: G.f.: x^2(1+4x+26x^2+19x^3+4x^5+x^6+26x^4)/((1+x)^4(1-x)^5). 
               [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 29 2008]
%e A145920 35, for example, is both A000326(5) and A000332(7).
%Y A145920 Cf. A141919, of which this is a subsequence.
%Y A145920 Sequence in context: A117985 A115707 A117793 this_sequence A153785 A090294 
               A162540
%Y A145920 Adjacent sequences: A145917 A145918 A145919 this_sequence A145921 A145922 
               A145923
%K A145920 easy,nonn
%O A145920 1,3
%A A145920 Matthew Vandermast (ghodges14(AT)comcast.net), Oct 28 2008

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