A130656 Interlacing n^3/2 and n^2(n + 1)/2.

1, 4, 18, 32, 75, 108, 196, 256, 405, 500, 726, 864, 1183, 1372, 1800, 2048, 2601, 2916, 3610, 4000, 4851, 5324, 6348, 6912, 8125, 8788, 10206, 10976, 12615, 13500, 15376, 16384, 18513, 19652, 22050, 23328, 26011, 27436, 30420, 32000, 35301, 37044

Offset

1,2

Links

Table of n, a(n) for n=1..42.

Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).

Formula

a(n) = n^2 * floor((n + 1)/2).

G.f.: x*(1+3*x+11*x^2+5*x^3+4*x^4)/((1-x)^4*(1+x)^3). - R. J. Mathar, Sep 09 2008

a(n) = a(n-1)+ 3*a(n-2)-3*a(n-3)-3*a(n-4)+3*a(n-5)+a(n-6)-a(n-7), a(1)=1, a(2)=4, a(3)=18, a(4)=32, a(5)=75, a(6)=108, a(7)=196. - Harvey P. Dale, Feb 18 2015

Sum_{n>=1} 1/a(n) = zeta(3)/4 + Pi^2/4 - 2*log(2). - Amiram Eldar, Mar 15 2024

Maple

A130656:=n->n^2 * floor((n + 1)/2): seq(A130656(n), n=1..100); # Wesley Ivan Hurt, Jan 21 2017

Mathematica

a[n_Integer] := n^2 * Floor[(n + 1)/2]
LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 4, 18, 32, 75, 108, 196}, 50] (* Harvey P. Dale, Feb 18 2015 *)

Crossrefs

Cf. A093005 (quadratic equivalent), A065423 (linear equivalent).

Sequence in context: A120407 A033166 A049726 * A292161 A346866 A363640

Adjacent sequences: A130653 A130654 A130655 * A130657 A130658 A130659

Keyword

easy,nonn

Author

Olivier Gérard, Jun 21 2007

Status

approved