The On-Line Encyclopedia of Integer Sequences (OEIS)

Revisions by Mats Granvik (See also Mats Granvik's wiki page)

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

A380385

Triangle read by rows. T(1, 1) = 1, T(n, k) = [n >= k](Sum_{i=1..k-1} T[n - i, k - 1] - Sum_{i=1..n-1} T[n - i, k]).
(history; published version)

#19 by Mats Granvik at Sat Jan 25 12:59:35 EST 2025

STATUS

editing

proposed

#18 by Mats Granvik at Sat Jan 25 12:59:32 EST 2025

MATHEMATICA

nn = 12; Table[Table[If[n == k, 1, Coefficient[Product[(1 - x^i), {i, k - 1}], x^(n - k)]], {k, 1, n}], {n, 1, nn}] // Flatten (* After Conjectured after A231599. - Mats Granvik, Jan 25 2025 *)

STATUS

proposed

editing

#17 by Mats Granvik at Sat Jan 25 12:53:04 EST 2025

STATUS

editing

proposed

#16 by Mats Granvik at Sat Jan 25 12:52:46 EST 2025

CROSSREFS

Cf. A231599, A010815, A008284.

STATUS

proposed

editing

#15 by Mats Granvik at Sat Jan 25 12:50:11 EST 2025

STATUS

editing

proposed

#14 by Mats Granvik at Sat Jan 25 12:49:54 EST 2025

MATHEMATICA

nn = 12; Table[Table[If[n == k, 1, Coefficient[Product[(1 - x^i), {i, k - 1}], x^(n - k)]], {k, 1, n}], {n, 1, nn}] // Flatten (* After A231599. - Mats Granvik, Jan 25 2025 *)

STATUS

approved

editing

A010815

From Euler's Pentagonal Theorem: coefficient of q^n in Product_{m>=1} (1 - q^m).
(history; published version)

#216 by Mats Granvik at Sat Jan 25 09:53:43 EST 2025

STATUS

editing

proposed

#215 by Mats Granvik at Sat Jan 25 09:53:31 EST 2025

FORMULA

a(n) = -Sum_{k=1..n} A380385(n, k), for n >= 1. - Mats Granvik, Jan 25 2025

STATUS

proposed

editing

#214 by Mats Granvik at Sat Jan 25 09:42:30 EST 2025

STATUS

editing

proposed

Discussion

Sat Jan 25

09:51

Joerg Arndt: does IMO not belong here; over in A380385 you say "appears to be", here you state as a fact.

#213 by Mats Granvik at Sat Jan 25 09:41:56 EST 2025

FORMULA

a(n) = -Sum_{k=1..n} A380385(n, k), for n >= 1. _- _Mats Granvik_, Jan 25 2025