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#60 by Gus Wiseman at Fri Feb 25 11:31:49 EST 2022
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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
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#59 by Gus Wiseman at Fri Feb 25 11:27:29 EST 2022
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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)
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proposed
editing
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#58 by Gus Wiseman at Fri Feb 25 11:11:01 EST 2022
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Discussion
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Fri Feb 25
| 11:14
| Gus Wiseman: Just curious, why do you put Mathematica in caps?
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| 11:16
| Gus Wiseman: Oh never mind, I see you probably copied it from the margin.
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#57 by Gus Wiseman at Fri Feb 25 11:10:44 EST 2022
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| MATHEMATICA
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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 *)
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proposed
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#56 by Michel Marcus at Fri Feb 25 08:19:59 EST 2022
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Discussion
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Fri Feb 25
| 08:40
| Alois P. Heinz: I cannot see that the new MATHEMATICA program is efficient ... so why should it be here?
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| 11:10
| Gus Wiseman: It's constructive. But not important, so I'll remove it.
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#55 by Michel Marcus at Fri Feb 25 08:19:56 EST 2022
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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
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proposed
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#54 by Gus Wiseman at Fri Feb 25 06:03:22 EST 2022
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#53 by Gus Wiseman at Fri Feb 25 06:02:53 EST 2022
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The ordered version (compositions) appears to beis A239327.
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#52 by Gus Wiseman at Fri Feb 25 05:56:16 EST 2022
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This appears isto apparentlybe the alternately equal case of A122130.
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#51 by Gus Wiseman at Fri Feb 25 05:53:26 EST 2022
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