A210956 - OEIS

%I #17 Feb 19 2020 20:13:16

%S 1,1,3,2,2,5,3,7,7,11,5,7,10,10,15,7,15,21,25,25,31,11,17,23,27,32,32,

%T 39,15,31,40,52,57,63,63,71,22,36,54,62,72,78,85,85,94,30,60,78,98,

%U 113,125,132,140,140,150,42,72,102,122,142,154,168,176,185,185,196

%N Triangle read by rows: T(n,k) = sum of all parts <= k in the last section of the set of partitions of n.

%C Row n lists the partial sums of row n of triangle A207383.

%H Andrew Howroyd, <a href="/A210956/b210956.txt">Table of n, a(n) for n = 1..1275</a>

%F T(n,k) = Sum_{j=1..k} A207383(n,j).

%e Triangle begins:

%e 1;

%e 1,   3;

%e 2,   2, 5;

%e 3,   7, 7, 11;

%e 5,   7, 10, 10, 15;

%e 7,  15, 21, 25, 25, 31;

%e 11, 17, 23, 27, 32, 32, 39;

%e 15, 31, 40, 52, 57, 63, 63, 71;

%e 22, 36, 54, 62, 72, 78, 85, 85, 94;

%o (PARI) Row(n)={my(v=vector(n)); v[1]=numbpart(n-1); if(n>1, forpart(p=n, for(k=1, #p, v[p[k]]++), [2,n])); for(k=2, n, v[k]=v[k-1]+k*v[k]); v}

%o { for(n=1, 10, print(Row(n))) }

%Y Column 1 is A000041. Right border gives A138879.

%Y Cf. A135010, A138121, A182703, A206437, A206562, A207031, A207032, 207383, 208476, A210948, A210955.

%K nonn,tabl

%O 1,3

%A _Omar E. Pol_, May 01 2012

%E Terms a(46) and beyond from _Andrew Howroyd_, Feb 19 2020