STATUS
proposed
approved
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Revision History for A347588
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STATUS
editing
proposed
NAME
allocated for Ilya GutkovskiyNumber of partitions of n into at most 6 distinct parts.
DATA
1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, 46, 54, 64, 76, 89, 104, 122, 142, 165, 192, 221, 255, 294, 337, 385, 441, 501, 570, 646, 731, 824, 930, 1043, 1171, 1310, 1464, 1630, 1817, 2015, 2236, 2473, 2734, 3013, 3322, 3648, 4008, 4391, 4809, 5252, 5738, 6249
OFFSET
0,4
LINKS
<a href="/index/Rec#order_21">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,0,0,-1,0,-2,0,1,1,1,1,0,-2,0,-1,0,0,1,1,-1).
FORMULA
G.f.: Sum_{k=0..6} x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j).
MATHEMATICA
nmax = 58; CoefficientList[Series[Sum[x^(k (k + 1)/2)/Product[(1 - x^j), {j, 1, k}], {k, 0, 6}], {x, 0, nmax}], x]
Join[{1}, LinearRecurrence[{1, 1, 0, 0, -1, 0, -2, 0, 1, 1, 1, 1, 0, -2, 0, -1, 0, 0, 1, 1, -1}, {1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, 46, 54, 64, 76}, 58]]
KEYWORD
allocated
nonn,easy
AUTHOR
Ilya Gutkovskiy, Sep 08 2021
STATUS
approved
editing
NAME
allocated for Ilya Gutkovskiy
KEYWORD
allocated
STATUS
approved