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

1,3

Comments

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

Links

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

Formula

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

Example

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;

Prog

(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))) }

Crossrefs

Column 1 is A000041. Right border gives A138879.

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

Sequence in context: A151842 A076118 A309045 * A282161 A205675 A342331

Adjacent sequences: A210953 A210954 A210955 * A210957 A210958 A210959

Keyword

nonn,tabl

Author

Omar E. Pol, May 01 2012

Extensions

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

Status

approved