login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A026740
a(n) = 2^n*(2^n - 1)*(2^n - 2)/6.
1
0, 0, 4, 56, 560, 4960, 41664, 341376, 2763520, 22238720, 178433024, 1429559296, 11444858880, 91592417280, 732873539584, 5863525154816, 46910348656640, 375291379056640, 3002365391929344, 24019060573863936, 192153034345676800, 1537226473786572800
OFFSET
0,3
LINKS
J. Brandts and C. Cihangir, Counting triangles that share their vertices with the unit n-cube, in Conference Applications of Mathematics 2013 in honor of the 70th birthday of Karel Segeth. Jan Brandts, Sergey Korotov, et al., eds., Institute of Mathematics AS CR, Prague 2013.
FORMULA
a(n) = binomial(2^n, 3).
a(n) = 14*a(n-1) - 56*a(n-2) + 64*a(n-3) for n>=3. - Harvey P. Dale, Jun 20 2012
MAPLE
seq(binomial(2^n, 3), n=0..20); # Zerinvary Lajos, Feb 22 2008
MATHEMATICA
Binomial[2^Range[0, 20], 3] (* or *) LinearRecurrence[{14, -56, 64}, {0, 0, 4}, 21] (* Harvey P. Dale, Jun 20 2012 *)
PROG
(Magma) [2^n*(2^n-1)*(2^n-2)/6: n in [0..20] ]; // Vincenzo Librandi, May 23 2011
(PARI) vector(20, n, binomial(2^(n-1), 6) ) \\ G. C. Greubel, Oct 26 2019
(Sage) [binomial(2^n, 6) for n in (0..20)] # G. C. Greubel, Oct 26 2019
(GAP) List([0..20], n-> Binomial(2^n, 3) ); # G. C. Greubel, Oct 26 2019
CROSSREFS
Sequence in context: A101540 A358882 A224181 * A191466 A333294 A130219
KEYWORD
nonn
STATUS
approved