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A369628
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Number of solutions to k_1 + 2*k_2 + ... + n*k_n = 1, where k_i are from {-1,0,1}, i=1..n.
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4
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0, 1, 2, 3, 6, 15, 36, 85, 213, 549, 1423, 3723, 9882, 26508, 71579, 194533, 532120, 1463561, 4044075, 11221727, 31260192, 87386579, 245058185, 689209348, 1943530845, 5494106583, 15566303698, 44196212866, 125727934145, 358317169828, 1022916667066, 2924843243594
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = [x^1] Product_{k=1..n} (x^k + 1 + 1/x^k).
a(n) = [x^(n*(n+1)/2+1)] Product_{k=1..n} (1 + x^k + x^(2*k)).
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MATHEMATICA
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Table[Coefficient[Product[(x^k + 1 + 1/x^k), {k, 1, n}], x, 1], {n, 0, 31}]
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PROG
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(Python)
from itertools import count, islice
from collections import Counter
def A369628_gen(): # generator of terms
ccount = Counter({0:1})
yield 0
for i in count(1):
bcount = Counter(ccount)
for a in ccount:
bcount[a+i] += ccount[a]
bcount[a-i] += ccount[a]
ccount = bcount
yield(ccount[1])
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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