A191484 - OEIS

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A191484

Number of compositions of even natural numbers into 5 parts <=n

1, 16, 122, 512, 1563, 3888, 8404, 16384, 29525, 50000, 80526, 124416, 185647, 268912, 379688, 524288, 709929, 944784, 1238050, 1600000, 2042051, 2576816, 3218172, 3981312, 4882813, 5940688 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,2`
	COMMENTS	`Number of ways of placing an even number of indistinguishable objects in 5 distinguishable boxes with the condition that in each box can be at most n objects`
	LINKS	`Vincenzo Librandi, Table of n, a(n) for n = 0..1000` `Adi Dani, Restricted compositions of natural numbers` `Index to sequences with linear recurrences with constant coefficients, signature (5,-9,5,5,-9,5,-1).`
	FORMULA	`a(n)= ((n + 1)^5 + (1 + (-1)^n)/2 )/2.` `a(n) = +5a(n-1) -9a(n-2) +5a(n-3) +5a(n-4) -9a(n-5) +5a(n-6) -1a(n-7)` `G.f.: (16x^4 + 41x^3 + 51x^2 + 11x + 1)/((1-x)^6(1+x))`
	EXAMPLE	`a(1)=16 as there are 16 compositions of even natural numbers into 5 parts <=1:` `(0,0,0,0,0);` `(0,0,0,1,1), (0,0,1,0,1), (0,0,1,1,0), (0,1,1,0,0), (0,1,0,1,0), (0,1,0,0,1), (1,1,0,0,0), (1,0,1,0,0), (1,0,0,1,0), (1,0,0,0,1);` `(0,1,1,1,1), (1,0,1,1,1), (1,1,0,1,1), (1,1,1,0,1), (1,1,1,1,0).`
	MATHEMATICA	`Table[1/2((n + 1)^5 + (1 + (-1)^n)1/2), {n, 0, 25}]` `LinearRecurrence[{5, -9, 5, 5, -9, 5, -1}, {1, 16, 122, 512, 1563, 3888, 8404}, 50] (* From Harvey P. Dale, Nov 09 2011 *)`
	PROG	`(MAGMA) [((n + 1)^5 + (1 + (-1)^n)/2 )/2: n in [0..40]]; // Vincenzo Librandi, Jun 16 2011`
	CROSSREFS	`Sequence in context: A104265 A068880 A053883 * A030508 A006215 A060633` `Adjacent sequences: A191481 A191482 A191483 * A191485 A191486 A191487`
	KEYWORD	`nonn`
	AUTHOR	`Adi Dani, Jun 03 2011`
	STATUS	`approved`

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Last modified May 18 04:49 EDT 2013. Contains 225419 sequences.