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A191967 n * (numbers that are not divisible by 3).

%I A191967 #27 Feb 16 2025 08:33:15
%S A191967 0,1,4,12,20,35,48,70,88,117,140,176,204,247,280,330,368,425,468,532,
%T A191967 580,651,704,782,840,925,988,1080,1148,1247,1320,1426,1504,1617,1700,
%U A191967 1820,1908,2035,2128,2262,2360,2501,2604,2752,2860,3015,3128,3290,3408
%N A191967 n * (numbers that are not divisible by 3).
%C A191967 A033579 and A033570 interleaved.
%H A191967 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentagonalNumber.html">Pentagonal Number</a>.
%H A191967 Wikipedia, <a href="http://en.wikipedia.org/wiki/Pentagonal_number">Pentagonal number</a>.
%H A191967 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (1,2,-2,-1,1).
%F A191967 a(n) = n * A001651(n).
%F A191967 a(n) = A000326(n) - A142150(n).
%F A191967 a(2*n) = A033579(n) = 4 * A000326(n);
%F A191967 a(2*n+1) = A033570(n) = A000326(2*n+1).
%F A191967 G.f.: x*(1+3*x+6*x^2+2*x^3)/((1+x)^2*(1-x)^3). - _Bruno Berselli_, Jul 09 2012
%F A191967 a(n) = A182079(3n). - _Bruno Berselli_, Jul 09 2012
%F A191967 From _Amiram Eldar_, Feb 18 2022: (Start)
%F A191967 Sum_{n>=1} 1/a(n) = Pi/(4*sqrt(3)) + 9*log(3)/4 - 2*log(2).
%F A191967 Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(3)*Pi/4 + 3*log(3)/4 - 2*log(2). (End)
%t A191967 Table[n (6 n - 3 - (-1)^n)/4, {n, 0, 48}] (* _Bruno Berselli_, Jul 09 2012 *)
%o A191967 (Haskell)
%o A191967 a191967 n = n * a001651 n
%o A191967 (Magma) A001651:=func<n|(6*n-3-(-1)^n)/4>; [n*A001651(n): n in [0..48]]; // _Bruno Berselli_, Jul 09 2012
%o A191967 (PARI) a(n)=n\2*3*n+if(n%2,n,-n) \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A191967 Cf. A000326, A001651, A033570, A033579, A142150, A182079.
%K A191967 nonn,easy
%O A191967 0,3
%A A191967 _Reinhard Zumkeller_, Jul 07 2012