The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A354127 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A354127

Triangle read by rows: T(n, k) is the number of graphs obtained by adding k pierced circles to a path graph P_n.
(history; published version)

#14 by Peter Luschny at Sat May 28 12:48:08 EDT 2022

STATUS

proposed

approved

#13 by Stefano Spezia at Sat May 28 11:52:34 EDT 2022

STATUS

editing

proposed

#12 by Stefano Spezia at Sat May 28 11:52:12 EDT 2022

FORMULA

T(n, n-2) = A006331(n-1).

CROSSREFS

Cf. A000007 (k = n), A000027 (k = n - 1), A000108, A001246 (row sums), A006331, A007318, A052553.

STATUS

proposed

editing

#11 by Stefano Spezia at Sat May 28 02:18:16 EDT 2022

STATUS

editing

proposed

#10 by Stefano Spezia at Sat May 28 02:18:00 EDT 2022

MATHEMATICA

ObigO[k_, s_]:=Binomial[2s-k-1, k]CatalanNumber[s-k]^2; T[n_, k_]:=Sum[(-1)^(m+k)Binomial[m, k]ObigO[m, n], {m, k, n}]; Flatten[Table[T[n, k], {n, 0, 9}, {k, 0, n}]]

STATUS

proposed

editing

Discussion

Sat May 28

02:18

Stefano Spezia: Fixed! Thanks much Peter

#9 by Stefano Spezia at Sat May 28 00:44:57 EDT 2022

STATUS

editing

proposed

Discussion

Sat May 28

00:50

Stefano Spezia: Thanks

02:07

Peter Luschny: How does this work? Tag O in O[k_, s_] is protected.

#8 by Stefano Spezia at Sat May 28 00:42:46 EDT 2022

CROSSREFS

Cf. A000108, A001246 (row sums), A007318, A052553, A354128, A354129.

STATUS

proposed

editing

Discussion

Sat May 28

00:44

Stefano Spezia: You are right! They don’t appear in the asymptotic grow. I inserted because they have the same reference link. I removed them now

#7 by Stefano Spezia at Wed May 18 09:36:02 EDT 2022

STATUS

editing

proposed

Discussion

Fri May 27

22:29

Jianing Song: Sorry but I don't understand why Cf. A354128, A354129. Do those constants appear, say, in the asymptotic growth of this one?

#6 by Stefano Spezia at Wed May 18 09:35:36 EDT 2022

EXAMPLE

2, 2, 0;

12, 10, 3, 0;

82, 82, 28, 4, 0;

646, 738, 315, 60, 5, 0;

#5 by Stefano Spezia at Wed May 18 09:34:14 EDT 2022

CROSSREFS

Cf. A000108, A001246 (row sums), A007318, A052553, A354128, A354129.