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Revision History for A053251 (Underlined text is an addition; strikethrough text is a deletion.)

newer changes | Showing entries 11-20 | older changes
A053251 Coefficients of the '3rd-order' mock theta function psi(q)
(history; published version)
#60 by Gus Wiseman at Fri Feb 25 11:31:49 EST 2022
COMMENTS

For Emeric Deutsch's comment above, (1) this appears to be thean alternately equal case of A122130, (2) the ordered version (compositions) is A239327, (3) allowing any length gives A351006, (4) the even-length version is A351007. - Gus Wiseman, Feb 25 2022

#59 by Gus Wiseman at Fri Feb 25 11:27:29 EST 2022
COMMENTS

From _For Emeric Deutsch's comment above, (1) this appears to be the alternately equal case of A122130, (2) the ordered version (compositions) is A239327, (3) allowing any length gives A351006, (4) the even-length version is A351007. - _Gus Wiseman_, Feb 2225 2022: (Start)

Also the number of odd-length integer partitions of n into parts that are alternately unequal and equal. For example, the a(1) = 1 through a(9) = 7 partitions are (A..D = 10..13):

1 2 3 4 5 6 7 8 9 A B C D

211 311 411 322 422 522 433 533 633 544

511 611 711 622 722 822 733

32211 811 911 A11 922

42211 52211 43311 B11

62211 53311

72211

This appears to be the alternately equal case of A122130.

The ordered version (compositions) is A239327.

Allowing any length gives A351006.

The even-length version is A351007.

(End)

STATUS

proposed

editing

#58 by Gus Wiseman at Fri Feb 25 11:11:01 EST 2022
STATUS

editing

proposed

Discussion
Fri Feb 25 11:14
Gus Wiseman: Just curious, why do you put Mathematica in caps?
11:16
Gus Wiseman: Oh never mind, I see you probably copied it from the margin.
#57 by Gus Wiseman at Fri Feb 25 11:10:44 EST 2022
MATHEMATICA

Table[Length[Select[IntegerPartitions[n], OddQ[Length[#]]&&And@@Table[If[EvenQ[i], #[[i]]==#[[i+1]], #[[i]]!=#[[i+1]]], {i, Length[#]-1}]&]], {n, 0, 30}] (* Gus Wiseman, Feb 22 2022 *)

STATUS

proposed

editing

#56 by Michel Marcus at Fri Feb 25 08:19:59 EST 2022
STATUS

editing

proposed

Discussion
Fri Feb 25 08:40
Alois P. Heinz: I cannot see that the new MATHEMATICA program is efficient ... so why should it be here?
11:10
Gus Wiseman: It's constructive. But not important, so I'll remove it.
#55 by Michel Marcus at Fri Feb 25 08:19:56 EST 2022
COMMENTS

Number of different partial sums of 1+[1,3]+[1,5]+[1,7]+[1,9]+... E.g. a(6)=2 because we have 6=1+1+1+1+1+1=1+1+3+1 - _. - _Jon Perry_, Jan 01 2004

STATUS

proposed

editing

#54 by Gus Wiseman at Fri Feb 25 06:03:22 EST 2022
STATUS

editing

proposed

#53 by Gus Wiseman at Fri Feb 25 06:02:53 EST 2022
COMMENTS

The ordered version (compositions) appears to beis A239327.

#52 by Gus Wiseman at Fri Feb 25 05:56:16 EST 2022
COMMENTS

This appears isto apparentlybe the alternately equal case of A122130.

#51 by Gus Wiseman at Fri Feb 25 05:53:26 EST 2022
CROSSREFS

Cf. A000070, A035363, A035457, A122129, A122130, A122134, A122135, A351003, A351005.

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Last modified August 30 21:20 EDT 2024. Contains 375548 sequences. (Running on oeis4.)