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A178932 Partitions into distinct parts where no subset of the summands is an arithmetic progression (of length 3 or more). 3
1, 1, 1, 2, 2, 3, 3, 5, 6, 6, 9, 11, 11, 15, 19, 18, 26, 29, 32, 38, 48, 47, 62, 68, 79, 89, 108, 110, 135, 152, 166, 191, 223, 237, 275, 306, 345, 380, 429, 472, 537, 588, 650, 721, 808, 902, 972, 1083, 1205, 1316, 1450, 1617, 1742, 1919, 2130, 2312, 2531 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(0) = 1 as is common practice with partitions.

LINKS

Fausto A. C. Cariboni, Table of n, a(n) for n = 0..400

Index entries related to non-averaging sequences

EXAMPLE

There are 4 partitions of 6 into distinct parts, 6, 5+1, 4+2, and 3+2+1.  Since 3+2+1 contains the arithmetic progression 3,2,1, it won't be counted here.  Thus a(6)=3.

PROG

(Sage) has_arith_prog = lambda x, size: any(len(set(differences(c))) <= 1 for c in Combinations(x, size))

A178932 = lambda n: Partitions(n, max_slope=-1).filter(lambda p: not has_arith_prog(sorted(p), 3)).cardinality() # [D. S. McNeil, Dec 31 2010]

CROSSREFS

Cf. A003407, A238569, A238571, A238687.

Sequence in context: A325876 A325468 A320347 * A325852 A332668 A206439

Adjacent sequences:  A178929 A178930 A178931 * A178933 A178934 A178935

KEYWORD

nonn

AUTHOR

David S. Newman, Dec 30 2010

STATUS

approved

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Last modified January 26 13:18 EST 2021. Contains 340439 sequences. (Running on oeis4.)