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A172242 Number of 10-D hypercubes in an n-dimensional hypercube. 3
1, 22, 264, 2288, 16016, 96096, 512512, 2489344, 11202048, 47297536, 189190144, 722362368, 2648662016, 9372188672, 32133218304, 107110727680, 348109864960, 1105760747520, 3440144547840, 10501493882880, 31504481648640 (list; graph; refs; listen; history; text; internal format)
OFFSET
10,2
COMMENTS
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.
LINKS
Milan Janjic and Boris Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.
Index entries for linear recurrences with constant coefficients, signature (22,-220,1320,-5280,14784,-29568,42240,-42240,28160,-11264,2048).
FORMULA
a(n) = A038207(n,10).
a(n) = binomial(n,10)*2^(n-10). [Corrected by R. J. Mathar, Feb 21 2010]
G.f.: -x^10/(2*x-1)^11. - Colin Barker, Nov 11 2012
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
From Amiram Eldar, Jan 07 2022: (Start)
Sum_{n>=10} 1/a(n) = 1879/126 - 20*log(2).
Sum_{n>=10} (-1)^n/a(n) = 393660*log(3/2) - 20111419/126. (End)
MATHEMATICA
Table[Binomial[n + 10, 10]*2^n, {n, 0, 22}]
PROG
(Sage)[lucas_number2(n, 2, 0)*binomial(n, 10)/2^10 for n in range(10, 31)] # Zerinvary Lajos, Feb 05 2010
CROSSREFS
Sequence in context: A143479 A213352 A004412 * A055756 A128766 A278153
KEYWORD
nonn,easy
AUTHOR
Zerinvary Lajos, Jan 29 2010
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)