A210956 Triangle read by rows: T(n,k) = sum of all parts <= k in the last section of the set of partitions of n.

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, 39, 15, 31, 40, 52, 57, 63, 63, 71, 22, 36, 54, 62, 72, 78, 85, 85, 94, 30, 60, 78, 98, 113, 125, 132, 140, 140, 150, 42, 72, 102, 122, 142, 154, 168, 176, 185, 185, 196

Offset: 1

Author

Omar E. Pol, May 01 2012

Keywords

• nonn
• tabl

Comments

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

Examples

			Triangle begins:
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, 39;
15, 31, 40, 52, 57, 63, 63, 71;
22, 36, 54, 62, 72, 78, 85, 85, 94;
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..1275

Crossrefs

Column 1 is A000041. Right border gives A138879.

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

Programs

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

Formula

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

Extensions

Terms a(46) and beyond from Andrew Howroyd, Feb 19 2020