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A011972 Sequence formed by reading rows of triangle defined in A011971. 5
1, 2, 3, 5, 7, 10, 15, 20, 27, 37, 52, 67, 87, 114, 151, 203, 255, 322, 409, 523, 674, 877, 1080, 1335, 1657, 2066, 2589, 3263, 4140, 5017, 6097, 7432, 9089, 11155, 13744, 17007, 21147, 25287, 30304, 36401, 43833, 52922, 64077, 77821, 94828 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Terms that are repeated in A011971 are included only once. In other words, dropping the elements on the diagonal and reading by rows gives this sequence. [Joerg Arndt, May 31 2013]
LINKS
EXAMPLE
Triangle T(n, k) begins:
[0] 1;
[1] 2, 3;
[2] 5, 7, 10;
[3] 15, 20, 27, 37;
[4] 52, 67, 87, 114, 151;
[5] 203, 255, 322, 409, 523, 674;
[6] 877, 1080, 1335, 1657, 2066, 2589, 3263;
...
MAPLE
T := (n, k) -> local i; add(binomial(k, i)*combinat:-bell(n - k + i + 1), i = 0..k): seq(seq(T(n, k), k=0..n), n = 0..9); # Peter Luschny, Dec 02 2023
MATHEMATICA
T[n_, k_] := Sum[Binomial[k, i] BellB[n - k + i + 1], {i, 0, k}];
Table[T[n, k], {n, 0, 8}, {k, 0, n}] // Flatten (* Jean-François Alcover, Nov 19 2019 *)
PROG
(Python)
from itertools import accumulate
A011972_list = blist = [1]
for _ in range(10**2):
b = blist[-1]
blist = list(accumulate([b]+blist))
A011972_list += blist[1:]
# Chai Wah Wu, Sep 02 2014, updated Chai Wah Wu, Sep 20 2014
CROSSREFS
Sequence in context: A092021 A022475 A330937 * A338553 A272402 A321176
KEYWORD
nonn,easy,tabl
AUTHOR
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)