A231559 a(n) = floor( A000326(n)/2 ).

0, 0, 2, 6, 11, 17, 25, 35, 46, 58, 72, 88, 105, 123, 143, 165, 188, 212, 238, 266, 295, 325, 357, 391, 426, 462, 500, 540, 581, 623, 667, 713, 760, 808, 858, 910, 963, 1017, 1073, 1131, 1190, 1250, 1312, 1376, 1441, 1507, 1575, 1645, 1716, 1788, 1862, 1938

Offset: 0

Author

Bruno Berselli, Nov 11 2013

Keywords

• nonn
• easy

Comments

First trisection of A011865.

Links

• Bruno Berselli, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-4,4,-3,1).

Crossrefs

Cf. pentagonal numbers: A000326.

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

First differences: A047262.

Programs

Magma

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

Mathematica

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

Formula

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

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