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Identifier

St000382: Integer compositions ⟶ ℤ

Values

[1] => 1

[1,1] => 1

[2] => 2

[1,1,1] => 1

[1,2] => 1

[2,1] => 2

[3] => 3

[1,1,1,1] => 1

[1,1,2] => 1

[1,2,1] => 1

[1,3] => 1

[2,1,1] => 2

[2,2] => 2

[3,1] => 3

[4] => 4

[1,1,1,1,1] => 1

[1,1,1,2] => 1

[1,1,2,1] => 1

[1,1,3] => 1

[1,2,1,1] => 1

[1,2,2] => 1

[1,3,1] => 1

[1,4] => 1

[2,1,1,1] => 2

[2,1,2] => 2

[2,2,1] => 2

[2,3] => 2

[3,1,1] => 3

[3,2] => 3

[4,1] => 4

[5] => 5

[1,1,1,1,1,1] => 1

[1,1,1,1,2] => 1

[1,1,1,2,1] => 1

[1,1,1,3] => 1

[1,1,2,1,1] => 1

[1,1,2,2] => 1

[1,1,3,1] => 1

[1,1,4] => 1

[1,2,1,1,1] => 1

[1,2,1,2] => 1

[1,2,2,1] => 1

[1,2,3] => 1

[1,3,1,1] => 1

[1,3,2] => 1

[1,4,1] => 1

[1,5] => 1

[2,1,1,1,1] => 2

[2,1,1,2] => 2

[2,1,2,1] => 2

[2,1,3] => 2

[2,2,1,1] => 2

[2,2,2] => 2

[2,3,1] => 2

[2,4] => 2

[3,1,1,1] => 3

[3,1,2] => 3

[3,2,1] => 3

[3,3] => 3

[4,1,1] => 4

[4,2] => 4

[5,1] => 5

[6] => 6

[1,1,1,1,1,1,1] => 1

[1,1,1,1,1,2] => 1

[1,1,1,1,2,1] => 1

[1,1,1,1,3] => 1

[1,1,1,2,1,1] => 1

[1,1,1,2,2] => 1

[1,1,1,3,1] => 1

[1,1,1,4] => 1

[1,1,2,1,1,1] => 1

[1,1,2,1,2] => 1

[1,1,2,2,1] => 1

[1,1,2,3] => 1

[1,1,3,1,1] => 1

[1,1,3,2] => 1

[1,1,4,1] => 1

[1,1,5] => 1

[1,2,1,1,1,1] => 1

[1,2,1,1,2] => 1

[1,2,1,2,1] => 1

[1,2,1,3] => 1

[1,2,2,1,1] => 1

[1,2,2,2] => 1

[1,2,3,1] => 1

[1,2,4] => 1

[1,3,1,1,1] => 1

[1,3,1,2] => 1

[1,3,2,1] => 1

[1,3,3] => 1

[1,4,1,1] => 1

[1,4,2] => 1

[1,5,1] => 1

[1,6] => 1

[2,1,1,1,1,1] => 2

[2,1,1,1,2] => 2

[2,1,1,2,1] => 2

[2,1,1,3] => 2

[2,1,2,1,1] => 2

[2,1,2,2] => 2

>>> Load all 1323 entries. <<<

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$F_{1} = q$

$F_{2} = q + q^{2}$

$F_{3} = 2\ q + q^{2} + q^{3}$

$F_{4} = 4\ q + 2\ q^{2} + q^{3} + q^{4}$

$F_{5} = 8\ q + 4\ q^{2} + 2\ q^{3} + q^{4} + q^{5}$

$F_{6} = 16\ q + 8\ q^{2} + 4\ q^{3} + 2\ q^{4} + q^{5} + q^{6}$

$F_{7} = 32\ q + 16\ q^{2} + 8\ q^{3} + 4\ q^{4} + 2\ q^{5} + q^{6} + q^{7}$

$F_{8} = 64\ q + 32\ q^{2} + 16\ q^{3} + 8\ q^{4} + 4\ q^{5} + 2\ q^{6} + q^{7} + q^{8}$

$F_{9} = 128\ q + 64\ q^{2} + 32\ q^{3} + 16\ q^{4} + 8\ q^{5} + 4\ q^{6} + 2\ q^{7} + q^{8} + q^{9}$

Description

The first part of an integer composition.

Code

def statistic(comp):
    return comp[0]

Created

Feb 09, 2016 at 16:03 by Christian Stump

Updated

Sep 19, 2024 at 17:41 by Martin Rubey