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A102420 Number of partitions of n into exactly k = 5 parts with each part p <= 5. 2

%I

%S 0,0,0,0,0,1,1,2,3,5,6,8,9,11,11,12,11,11,9,8,6,5,3,2,1,1,0,0,0,0,0,0,

%T 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,

%U 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N Number of partitions of n into exactly k = 5 parts with each part p <= 5.

%C There are only 26 nonzero terms.

%C a(n) is also the number of partitions of n-1 into exactly 4 parts with each part p in the range 1 <= p <= 6; i.e. the number of ways of arriving at a total of n-1 with 4 6-sided dice. - _Toby Gottfried_, Feb 19 2009

%F G.f.:z^5+z^6+2*z^7+3*z^8+5*z^9+6*z^10+8*z^11+9*z^12+11*z^13 +11*z^14 +12*z^15+ 11*z^16+11*z^17+9*z^18+8*z^19+6*z^20+5*z^21+3*z^22 +2*z^23 +z^24 +z^25.

%e a(8) = 3 because we can write 8=1+1+1+2+3 or 1+1+1+1+4 or 1+1+2+2+2.

%t Table[Count[IntegerPartitions[n,{5}],_?(Max[#]<6&)],{n,0,110}] (* _Harvey P. Dale_, Nov 29 2012 *)

%Y Cf. A000041, A102422, A036606.

%K easy,nonn

%O 0,8

%A _Thomas Wieder_, Jan 09 2005

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Last modified October 20 05:42 EDT 2017. Contains 293601 sequences.