The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A141321 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A141321

a(n) = -A141055(n)/(n+1)!.
(history; published version)

#17 by Alois P. Heinz at Mon Dec 22 12:10:31 EST 2014

STATUS

proposed

approved

#16 by Jean-François Alcover at Mon Dec 22 10:55:55 EST 2014

STATUS

editing

proposed

Discussion

Mon Dec 22

11:07

Jean-François Alcover: I hope not to betray Paul's observations:
Jacobsthal numbers (except the first ones) appear 3 times (that is at 3 sequences of positions),
through their differences or multiplied by 2 or 4, signs alternating.
1)   1, -3,  5, -11, 21, ... at positions 0, 1, 3, 6, 10, 15, 21, 28, 36, 45, ... (triangulars).
2)      -6, 10, -22, 42, ... at positions 4, 7, 11, 16, 22, 29, 37, 46, ... (shifted triangulars+1).
3)     -12, 20, -44, 84, ... at positions 8, 12, 17, 23, 30, 38, 47, ... (shifted triangulars+2).

11:11

Jean-François Alcover: Sorry, this comment was not for this sequence (I feel some fatigue ! )

12:10

Alois P. Heinz: it will be ignored.

#15 by Jean-François Alcover at Mon Dec 22 10:55:49 EST 2014

COMMENTS

a(n+1)/a(n)= 2/2, 30/3, 2/4, 42/5, 2/6, 30/7, 2/8, 66/9, 2/10, 2730/11, 2/12 = A027760(n+2)/(n+1), see A141410. Numerators are also (1, 2, 6, 2, 30, 2, ... = A141056)(n+3)).

STATUS

proposed

editing

#14 by Jean-François Alcover at Mon Dec 22 07:02:07 EST 2014

STATUS

editing

proposed

Discussion

Mon Dec 22

07:03

Jean-François Alcover: Edited comment

#13 by Jean-François Alcover at Mon Dec 22 07:00:18 EST 2014

COMMENTS

a(n+1)/a(n)= 2/2, 30/3, 2/4, 42/5, 2/6, 30/7, 2/8, 66/9, 2/10, 2730/11, 2/12 = A027760(n+2)/(n+1), see A141410. Numerators are also (1, 2, 6, 2, 30, 2, ... = A141056)(n+3);).

STATUS

proposed

editing

#12 by Jon E. Schoenfield at Fri Dec 19 08:58:17 EST 2014

STATUS

editing

proposed

#11 by Jon E. Schoenfield at Fri Dec 19 08:58:14 EST 2014

NAME

a(n) = -A141055(n)/(n+1)! .

COMMENTS

a(n+1)/a(n)= 2/2, 30/3, 2/4, 42/5, 2/6, 30/7, 2/8, 66/9, 2/10, 2730/11, 2/12 = A027760(n+2)/(n+1), see A141410. Numerators are also (1, 2, 6, 2, 30, 2=A141056)(n+3);

FORMULA

a(2n) / a(2n+1) = n + 1.

STATUS

proposed

editing

#10 by Joerg Arndt at Fri Dec 19 05:26:34 EST 2014

STATUS

editing

proposed

#9 by Joerg Arndt at Fri Dec 19 05:25:00 EST 2014

NAME

a(n) = -A141055(n)/(n+1)! .

COMMENTS

a(n+1)/a(n)= 2/2, 30/3, 2/4, 42/5, 2/6, 30/7, 2/8, 66/9, 2/10, 2730/11, 2/12 = A027760(n+2)/(n+1), see A141410. Numerators are also (1, 2, 6, 2, 30, 2=A141056)(n+3);

FORMULA

a(n+1)/a(n)= 2/2, 30/3, 2/4, 42/5, 2/6, 30/7, 2/8, 66/9, 2/10, 2730/11, 2/12 = A027760(n+2)/(n+1), see A141410. Numerators are also (1, 2, 6, 2, 30, 2=A141056)(n+3);

MAPLE

A141321 := proc(n) -A141055(n)/(n+1)! ; end proc: # _R. J. Mathar, _, Jul 08 2011

STATUS

proposed

editing

#8 by Jean-François Alcover at Thu Dec 18 09:29:35 EST 2014

STATUS

editing

proposed

Discussion

Thu Dec 18

12:45

Joerg Arndt: IMHO comments still need editing.

19:39

Jon E. Schoenfield: Should most of the Formula section be moved to Comments?