A231559 - OEIS

%I #21 Sep 08 2022 08:46:06

%S 0,0,2,6,11,17,25,35,46,58,72,88,105,123,143,165,188,212,238,266,295,

%T 325,357,391,426,462,500,540,581,623,667,713,760,808,858,910,963,1017,

%U 1073,1131,1190,1250,1312,1376,1441,1507,1575,1645,1716,1788,1862,1938

%N a(n) = floor( A000326(n)/2 ).

%C First trisection of A011865.

%H Bruno Berselli, <a href="/A231559/b231559.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (3,-4,4,-3,1).

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

%F a(n) = ( n*(3*n-1) + i^(n*(n+1)) - 1 )/4, where i=sqrt(-1).

%t Table[Floor[n (3 n - 1)/4], {n, 0, 60}]

%t CoefficientList[Series[x^2(2+x^2)/((1+x^2)(1-x)^3),{x,0,70}],x] (* or *) LinearRecurrence[{3,-4,4,-3,1},{0,0,2,6,11},70] (* _Harvey P. Dale_, Jan 28 2022 *)

%o (Magma) [Floor(n*(3*n-1)/4): n in [0..60]];

%Y Cf. pentagonal numbers: A000326.

%Y Cf. A011848 for the triangular numbers: floor(A000217/2); A007590 for the squares: floor(A000290/2); A156859 for the hexagonal numbers: floor(A000384/2).

%Y First differences: A047262.

%K nonn,easy

%O 0,3

%A _Bruno Berselli_, Nov 11 2013