OFFSET
0,2
COMMENTS
Number of ways of placing an even number of indistinguishable objects in 7 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
Index entries for linear recurrences with constant coefficients, signature (7,-20,28,-14,-14,28,-20,7,-1).
FORMULA
a(n) = ((n + 1)^7 + (1 + (-1)^n)/2 )/2.
G.f.: ( 1 + 57*x + 666*x^2 + 1786*x^3 + 1821*x^4 + 645*x^5 + 64*x^6 ) / ( (1+x)*(x-1)^8 ). - R. J. Mathar, Jun 08 2011
EXAMPLE
a(1)=64 and compositions of even natural numbers into 7 parts no greater than 1 are
:(0,0,0,0,0,0,0) --> 7!/7!0! = 1
:(0,0,0,0,0,1,1) --> 7!/5!2! = 21
:(0,0,0,1,1,1,1) --> 7!/3!4! = 35
:(0,1,1,1,1,1,1) --> 7!/1!6! = 7
MATHEMATICA
Table[1/2*((n + 1)^7 + (1 + (-1)^n)*1/2), {n, 0, 25}]
PROG
(Magma) [((n + 1)^7 + (1+(-1)^n)/2 )/2: n in [0..40]]; // Vincenzo Librandi, Jun 16 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Adi Dani, Jun 03 2011
STATUS
approved