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%I #17 Jun 13 2015 00:50:53
%S 0,1,1,6,7,22,27,62,77,147,182,308,378,588,714,1044,1254,1749,2079,
%T 2794,3289,4290,5005,6370,7371,9191,10556,12936,14756,17816,20196,
%U 24072,27132,31977,35853,41838,46683,53998,59983,68838,76153,86779,95634
%N An interleaved sequence of pyramidal and polygonal numbers.
%H Vincenzo Librandi, <a href="/A081284/b081284.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (2,3,-8,-2,12,-2,-8,3,2,-1).
%F G.f.: x*(1+x^3)/((1-x)*(1-x^2)^5).
%F a(2*n) = A005585(n); a(2*n+1) = A081282(n+1).
%F G.f.: (x*(x^2-x+1))/((x+1)^4*(x-1)^6). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 28 2009
%F a(n) = (2*n+1-(-1)^n)*(2*n+5-(-1)^n)*(2*n+9-(-1)^n)*(2*n^2+15*n+51+3*(n-5)*(-1)^n)/30720. - _Luce ETIENNE_, Mar 13 2015
%t CoefficientList[Series[x (1 + x^3) / ((1 - x) (1 - x^2)^5), {x, 0, 50}], x] (* _Vincenzo Librandi_, Aug 07 2013 *)
%Y Cf. A081283, A081282.
%K easy,nonn
%O 0,4
%A _Paul Barry_, Mar 17 2003
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