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A076276 Number of + signs needed to write the partitions of n (A000041) as sums. 5
0, 0, 1, 3, 7, 13, 24, 39, 64, 98, 150, 219, 322, 455, 645, 892, 1232, 1668, 2259, 3008, 4003, 5260, 6897, 8951, 11599, 14893, 19086, 24284, 30827, 38888, 48959, 61293, 76578, 95223, 118152, 145993, 180037, 221175, 271186, 331402, 404208, 491521 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,4
COMMENTS
Also, total number of parts in all partitions of n-1 plus the number of emergent parts of n, if n >= 1. Also, sum of largest parts of all partitions of n-1 plus the number of emergent parts of n, if n >= 1. - Omar E. Pol, Oct 30 2011
Also total number of parts that are not the largest part in all partitions of n. - Omar E. Pol, Apr 30 2012
Empirical: For n > 1, a(n) is the sum of the entries in the second column of the lower-triangular matrix of coefficients giving the expansion of degree-n complete homogeneous symmetric functions in the Schur basis of the algebra of symmetric functions. - John M. Campbell, Mar 18 2018
LINKS
FORMULA
a(n) = (Sum_{k=1..n} tau(k)*numbpart(n-k))-numbpart(n) = A006128(n)-A000041(n), n>0. - Vladeta Jovovic, Oct 06 2002
G.f.: sum(n>=1, (n-1) * x^n / prod(k=1,n, 1-x^k ) ). - Joerg Arndt, Apr 17 2011
a(n) = A006128(n-1) + A182699(n), n >= 1. - Omar E. Pol, Oct 30 2011
EXAMPLE
4=1+3=2+2=1+1+2=1+1+1+1, 7 + signs are needed, so a(4)=7.
MATHEMATICA
a[0]=0; a[n_] := Sum[DivisorSigma[0, k]PartitionsP[n-k], {k, 1, n}]-PartitionsP[n]
CROSSREFS
Sequence in context: A232533 A061263 A156209 * A296558 A309051 A056764
KEYWORD
nonn
AUTHOR
Floor van Lamoen, Oct 04 2002
EXTENSIONS
More terms from Vladeta Jovovic, Robert G. Wilson v, Dean Hickerson and Don Reble, Oct 06 2002
STATUS
approved

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Last modified May 19 12:47 EDT 2024. Contains 372692 sequences. (Running on oeis4.)