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A050442 Octahedral torus number: a(n) = n^2+2*sum(k^2,k=1..n-1)-2*(floor((n+1)/2)^2+2*sum(k^2,k=1..floor((n+1)/2)-1))+(1-(-1)^n)/2. 1
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 (list; graph; refs; listen; history; text; internal format)
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(1)=0, a(2)=4, a(3)=8, a(4)=32, a(5)=48, a(6)=108, a(7)=144, 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). [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

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Last modified July 4 16:24 EDT 2020. Contains 335448 sequences. (Running on oeis4.)