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A081283 An interleaved sequence of pyramidal and polygonal numbers. 3

%I

%S 0,1,1,5,6,16,20,40,50,85,105,161,196,280,336,456,540,705,825,1045,

%T 1210,1496,1716,2080,2366,2821,3185,3745,4200,4880,5440,6256,6936,

%U 7905,8721,9861,10830,12160,13300,14840,16170,17941,19481,21505,23276,25576,27600

%N An interleaved sequence of pyramidal and polygonal numbers.

%H Vincenzo Librandi, <a href="/A081283/b081283.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,2,-6,0,6,-2,-2,1).

%F G.f.: x*(1+x^3)/((1-x)*(1-x^2)^4).

%F a(2*n) = A002415(n); a(2*n+1) = A006007(n+1).

%F a(n) = (2*n+1-(-1)^n)*(2*n+5-(-1)^n)*(2*n^2+2*(5+(-1)^n)*n+27-11*(-1)^n)/1536. - _Luce ETIENNE_, Mar 11 2015

%p A081283:=n->(2*n+1-(-1)^n)*(2*n+5-(-1)^n)*(2*n^2+2*(5+(-1)^n)*n+27-11*(-1)^n)/1536: seq(A081283(n), n=0..80); # _Wesley Ivan Hurt_, Apr 18 2017

%t CoefficientList[Series[x (1 + x^3) / ((1 - x) (1 - x^2)^4), {x, 0, 50}], x] (* _Vincenzo Librandi_, Aug 07 2013 *)

%Y Cf. A081282, A081284.

%K easy,nonn

%O 0,4

%A _Paul Barry_, Mar 17 2003

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Last modified April 24 18:03 EDT 2019. Contains 322430 sequences. (Running on oeis4.)