1,3

Compositions ending in an even part yield sequence 0 1 2 6 18 ... (this sequence). and A123638(n)+a(n) = A047970(n). Ending parity of compositions can be detected using mod(A065120,2)

4

31 32 33

211 221 222

1111

Consider the above multisets- permute and note the parity of the ending part of each of the 14 compositions.

4

31 13 32 23 33

211 121 112 221 212 122 222

1111

4 is even

31 13 23 and 33 are odd

32 is even

etc

there are 1+1+4+0 even compositions therefore a(4)=6.

Cf. A001045 A047970 A065120 A123638 A123640 A123641.

Adjacent sequences: A123636 A123637 A123638 this_sequence A123640 A123641 A123642

Sequence in context: A085827 A000661 A079456 this_sequence A097635 A077630 A045962

more,nonn

Alford Arnold (Alford1940(AT)aol.com), Oct 04 2006