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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 Table of n, a(n) for n=0..41. 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 Cf. A001475, A248475. Sequence in context: A232533 A061263 A156209 * A296558 A309051 A056764 Adjacent sequences: A076273 A076274 A076275 * A076277 A076278 A076279 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.)