cp's OEIS Frontend

A172242 Number of 10-D hypercubes in an n-dimensional hypercube.

%I A172242 #33 Jan 07 2022 05:17:24
%S A172242 1,22,264,2288,16016,96096,512512,2489344,11202048,47297536,189190144,
%T A172242 722362368,2648662016,9372188672,32133218304,107110727680,
%U A172242 348109864960,1105760747520,3440144547840,10501493882880,31504481648640
%N A172242 Number of 10-D hypercubes in an n-dimensional hypercube.
%C A172242 With a different offset, number of n-permutations (n>=8) of 3 objects: u, v, z with repetition allowed, containing exactly ten (10) u's.
%H A172242 Milan Janjic and Boris Petkovic, <a href="http://arxiv.org/abs/1301.4550">A Counting Function</a>, arXiv 1301.4550 [math.CO], 2013.
%H A172242 <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (22,-220,1320,-5280,14784,-29568,42240,-42240,28160,-11264,2048).
%F A172242 a(n) = A038207(n,10).
%F A172242 a(n) = binomial(n,10)*2^(n-10). [Corrected by _R. J. Mathar_, Feb 21 2010]
%F A172242 G.f.: -x^10/(2*x-1)^11. - _Colin Barker_, Nov 11 2012
%F A172242 a(n) = Sum_{i=10..n} binomial(i,10)*binomial(n,i). Example: for n=15, a(15) = 1*3003 + 11*1365 + 66*455 + 286*105 + 1001*15 + 3003*1 = 96096. - _Bruno Berselli_, Mar 23 2018
%F A172242 From _Amiram Eldar_, Jan 07 2022: (Start)
%F A172242 Sum_{n>=10} 1/a(n) = 1879/126 - 20*log(2).
%F A172242 Sum_{n>=10} (-1)^n/a(n) = 393660*log(3/2) - 20111419/126. (End)
%t A172242 Table[Binomial[n + 10, 10]*2^n, {n, 0, 22}]
%o A172242 (Sage)[lucas_number2(n, 2, 0)*binomial(n,10)/2^10 for n in range(10, 31)] # _Zerinvary Lajos_, Feb 05 2010
%Y A172242 Cf. A001788, A001789, A003472, A038207, A054849, A002409, A140325, A054851, A140354.
%K A172242 nonn,easy
%O A172242 10,2
%A A172242 _Zerinvary Lajos_, Jan 29 2010