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 A024794 Number of 10's in all partitions of n. 13

%I

%S 0,0,0,0,0,0,0,0,0,1,1,2,3,5,7,11,15,22,30,43,57,79,104,140,183,242,

%T 312,407,520,670,849,1081,1359,1715,2141,2678,3322,4125,5085,6274,

%U 7691,9430,11502,14025,17024,20655,24959,30140,36270,43612,52274,62604,74763

%N Number of 10's in all partitions of n.

%C The sums of ten successive terms give A000070. - _Omar E. Pol_, Jul 12 2012

%C a(n) is also the difference between the sum of 10-th largest and the sum of 11-st largest elements in all partitions of n. - _Omar E. Pol_, Oct 25 2012

%H Alois P. Heinz, <a href="/A024794/b024794.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = A181187(n,10) - A181187(n,11). - _Omar E. Pol_, Oct 25 2012

%p b:= proc(n, i) option remember; local g;

%p if n=0 or i=1 then [1, 0]

%p else g:= `if`(i>n, [0\$2], b(n-i, i));

%p b(n, i-1) +g +[0, `if`(i=10, g[1], 0)]

%p fi

%p end:

%p a:= n-> b(n, n)[2]:

%p seq (a(n), n=1..100); # _Alois P. Heinz_, Oct 27 2012

%t << DiscreteMath`Combinatorica`; Table[ Count[ Flatten[ Partitions[n]], 10], {n, 1, 55} ]

%Y Cf. A066633, A024786, A024787, A024788, A024789, A024790, A024791, A024792, A024793.

%K nonn

%O 1,12

%A _Clark Kimberling_

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