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A365515
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Table read by antidiagonals upward: the n-th row gives the lexicographically earliest infinite B_n sequence starting from 0.
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13
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0, 0, 1, 0, 1, 2, 0, 1, 3, 3, 0, 1, 4, 7, 4, 0, 1, 5, 13, 12, 5, 0, 1, 6, 21, 32, 20, 6, 0, 1, 7, 31, 55, 71, 30, 7, 0, 1, 8, 43, 108, 153, 124, 44, 8, 0, 1, 9, 57, 154, 366, 368, 218, 65, 9, 0, 1, 10, 73, 256, 668, 926, 856, 375, 80, 10, 0, 1, 11, 91, 333, 1153, 2214, 2286, 1424, 572, 96, 11
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OFFSET
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1,6
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COMMENTS
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A B_n sequence is a sequence such that all sums a(x_1) + a(x_2) + ... + a(x_n) are distinct for 1 <= x_1 <= x_2 <= ... <= x_n. Analogous to A347570 except that here the B_n sequences start from a(1) = 0.
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LINKS
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FORMULA
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EXAMPLE
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Table begins:
n\k | 1 2 3 4 5 6 7 8 9
----+---------------------------------------------------
1 | 0, 1, 2, 3, 4, 5, 6, 7, 8, ...
2 | 0, 1, 3, 7, 12, 20, 30, 44, 65, ...
3 | 0, 1, 4, 13, 32, 71, 124, 218, 375, ...
4 | 0, 1, 5, 21, 55, 153, 368, 856, 1424, ...
5 | 0, 1, 6, 31, 108, 366, 926, 2286, 5733, ...
6 | 0, 1, 7, 43, 154, 668, 2214, 6876, 16864, ...
7 | 0, 1, 8, 57, 256, 1153, 4181, 14180, 47381, ...
8 | 0, 1, 9, 73, 333, 1822, 8043, 28296, 102042, ...
9 | 0, 1, 10, 91, 500, 3119, 13818, 59174, 211135, ...
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PROG
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(Python)
from itertools import count, islice, combinations_with_replacement
def A365515_gen(): # generator of terms
asets, alists, klist = [set()], [[]], [0]
while True:
for i in range(len(klist)-1, -1, -1):
kstart, alist, aset = klist[i], alists[i], asets[i]
for k in count(kstart):
bset = set()
for d in combinations_with_replacement(alist+[k], i):
if (m:=sum(d)+k) in aset:
break
bset.add(m)
else:
yield k
alists[i].append(k)
klist[i] = k+1
asets[i].update(bset)
break
klist.append(0)
asets.append(set())
alists.append([])
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CROSSREFS
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Cf. A001477 (n=1), A025582 (n=2), A051912 (n=3), A365300 (n=4), A365301 (n=5), A365302 (n=6), A365303 (n=7), A365304 (n=8), A365305 (n=9), A002061 (k=4), A369817 (k=5), A369818 (k=6), A369819 (k=7), A347570.
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KEYWORD
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AUTHOR
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STATUS
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approved
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