A050442 Octahedral torus number: a(n) = n^2 + 2*(Sum_{k=1..n-1} k^2) - 2*(floor((n+1)/2)^2 + 2*(Sum_{k=1..floor((n+1)/2)-1} k^2)) + (1 - (-1)^n)/2.

0, 4, 8, 32, 48, 108, 144, 256, 320, 500, 600, 864, 1008, 1372, 1568, 2048, 2304, 2916, 3240, 4000, 4400, 5324, 5808, 6912, 7488, 8788, 9464, 10976, 11760, 13500, 14400, 16384, 17408, 19652, 20808, 23328, 24624, 27436, 28880, 32000, 33600, 37044

Offset

1,2

Comments

a(n) = A005900(n) - 2*A005900(floor((n+1)/2)) + (1-(-1)^n)/2.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = (2*n^3+n)/3 - (2/3)*(2*floor((n+1)/2)^3 + floor((n+1)/2)) + (1-(-1)^n)/2.

G.f.: 4*x^2*(1+x+3*x^2+x^3)/(1-x)^4/(1+x)^3. - Colin Barker, Feb 12 2012

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)=0, a(2)=4, a(3)=8, a(4)=32, a(5)=48, a(6)=108, a(7)=144. - Harvey P. Dale, May 13 2012

Maple

A050442:=n->(2*n^3+n)/3-2/3*(2*floor((n+1)/2)^3+floor((n+1)/2))+(1-(-1)^n)/2: seq(A050442(n), n=1..50); # Wesley Ivan Hurt, Oct 10 2014

Mathematica

Rest[CoefficientList[Series[4 x^2 (1+x+3 x^2+x^3)/(1-x)^4/(1+x)^3, {x, 0, 50}], x]] (* or *) LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {0, 4, 8, 32, 48, 108, 144}, 50] (* Harvey P. Dale, May 13 2012 *)

Prog

(Magma) [(2*n^3+n)/3-2/3*(2*Floor((n+1)/2)^3+Floor((n+1)/2))+(1-(-1)^n)/2: n in [1..50]]; // Vincenzo Librandi, Feb 12 2012

Crossrefs

Cf. A005900 (octahedral numbers).

Sequence in context: A124143 A173617 A034041 * A229953 A331408 A291938

Adjacent sequences: A050439 A050440 A050441 * A050443 A050444 A050445

Keyword

nonn,easy,nice

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 23 1999

Status

approved