The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A122130 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A122130

Expansion of f(-x^4, -x^16) / psi(-x) in powers of x where psi() is a Ramanujan theta function and f(, ) is Ramanujan's general theta function.
(history; published version)

#27 by Michael De Vlieger at Mon Mar 14 08:45:35 EDT 2022

STATUS

reviewed

approved

#26 by Joerg Arndt at Mon Mar 14 02:48:10 EDT 2022

STATUS

proposed

reviewed

#25 by Gus Wiseman at Sun Mar 13 23:52:25 EDT 2022

STATUS

editing

proposed

#24 by Jon E. Schoenfield at Wed Feb 23 22:22:17 EST 2022

STATUS

proposed

editing

Discussion

Wed Feb 23

22:22

Jon E. Schoenfield: I'm sorry, I mistakenly thought this draft had been proposed for review.

23:05

Gus Wiseman: It's ready, just waiting for ref'd sequences like A351594, A351594 to be approved.

Thu Mar 10

05:26

OEIS Server: This sequence has not been edited or commented on for a week
yet is not proposed for review.  If it is ready for review, please
visit https://oeis.org/draft/A122130 and click the button that reads
"These changes are ready for review by an OEIS Editor."

Thanks.
  - The OEIS Server

17:12

Gus Wiseman: Waiting for A351594, A351594.

#23 by Jon E. Schoenfield at Wed Feb 23 21:59:47 EST 2022

STATUS

editing

proposed

#22 by Jon E. Schoenfield at Wed Feb 23 21:59:45 EST 2022

COMMENTS

This appears to be the number of odd-length alternately strict integer partitions of n + 1, i.e. , partitions y such that y_i != y_{i+1} for all odd i. For example, the a(1) = 1 through a(9) = 7 partitions are:

#21 by Gus Wiseman at Wed Feb 23 20:54:27 EST 2022

COMMENTS

The even-length version is A351008. Including even-length partitions appears to give A122129. Swapping strictly and weakly decreasing relations gives A351595. The constant instead of strict version is A351594.

#20 by Gus Wiseman at Wed Feb 23 20:51:59 EST 2022

CROSSREFS

Cf. `A016116, A035363, A035457, A053251, `A067661, A122129, A122134, A122135, `A351003, A351005, A351008.

#19 by Gus Wiseman at Mon Feb 21 18:09:18 EST 2022

COMMENTS

The ordered version (compositions) appears to be A000213, with even-length version essentially A135491is A351008. Including even-length partitions appears to give A122129.

The alternately equal case is A053251, any length A351006.

Allowing any length gives A122129, for equal instead of unequal A351004.

The even-length version is A351008.

CROSSREFS

Cf. `A016116, ~A027383, A035363, A035457, A053251, `A067661, ~A088218, A122129, A122134, A122135, `A349060, A351003, A351005, ~A351007.

#18 by Gus Wiseman at Sat Feb 19 16:59:26 EST 2022

COMMENTS

The ordered version (compositions) appears to be A000213, with even-length version essentially A135491.

CROSSREFS

Cf. A000070, `A016116, A018819, ~A027383, A035363, A035457, A067661, ~A088218, A096441, A101417, A122134, A122135, `A349060, A350842, A351003, A351005, ~A351007.