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A086144 a(n) = 2*A071640(n) - n. 3
1, 0, 1, 2, 3, 4, 5, 4, 3, 2, 1, 2, 3, 4, 3, 4, 5, 6, 5, 6, 5, 4, 5, 6, 5, 4, 3, 2, 3, 2, 1, 2, 3, 2, 3, 4, 5, 6, 7, 6, 7, 6, 7, 8, 7, 6, 5, 6, 7, 6, 7, 8, 9, 10, 9, 10, 9, 8, 7, 8, 9, 8, 9, 8, 7, 6, 7, 8, 9, 8, 9, 10, 11, 10, 9, 10, 11, 10, 9, 8, 9, 10, 11, 10, 11, 10, 11, 12, 13, 14 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

COMMENTS

It is conjectured that A071640(n)/n -> 1/2. - Benoit Cloitre

a(6671) < 0. - Peter Luschny, Oct 05 2011

LINKS

Table of n, a(n) for n=1..90.

MAPLE

A086144 := proc(n) option remember; if n=1 then 1 else

if combinat[numbpart](n) mod 2 = 1 then 1 else -1 fi;

% + A086144(n-1) fi end: seq(A086144(i), i=1..90); # Peter Luschny, Oct 05 2011

MATHEMATICA

a071640[n_] := Sum[Mod[PartitionsP[i], 2], {i, 1, n}];

a[n_] := 2 a071640[n] - n;

Array[a, 100] (* Jean-Fran├žois Alcover, Jun 11 2019 *)

PROG

(PARI) a(n) = my(x='x+O('x^(n+1)), p = 1/eta(x)); sum(i=1, n, (1-(-1)^(polcoeff(p, i)))) - n; \\ Michel Marcus, Jun 11 2019

CROSSREFS

Cf. A071640, A040051, A000041, A087177.

Sequence in context: A280913 A035343 A017880 * A131974 A181975 A062406

Adjacent sequences:  A086141 A086142 A086143 * A086145 A086146 A086147

KEYWORD

sign

AUTHOR

Benoit Cloitre, Sep 06 2003

EXTENSIONS

Erroneous data for n>55 replaced, keyword sign added by Peter Luschny, Oct 05 2011

STATUS

approved

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Last modified October 16 21:10 EDT 2019. Contains 328103 sequences. (Running on oeis4.)