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A210956 Triangle read by rows: T(n,k) = sum of all parts <= k in the last section of the set of partitions of n. 4
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 (list; table; graph; refs; listen; history; text; internal format)
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 A058608

Adjacent sequences:  A210953 A210954 A210955 * A210957 A210958 A210959

KEYWORD

nonn,tabl,changed

AUTHOR

Omar E. Pol, May 01 2012

EXTENSIONS

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

STATUS

approved

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Last modified February 23 04:49 EST 2020. Contains 332159 sequences. (Running on oeis4.)