Margaret Archibald has authored 3 sequences.
A335714
The sum of the sizes (positions) of fixed points over all compositions of n.
Original entry on oeis.org
1, 1, 4, 8, 19, 41, 89, 189, 398, 830, 1719, 3539, 7251, 14797, 30096, 61044, 123531, 249501, 503117, 1013165, 2037986, 4095546, 8223919, 16502823, 33097639, 66349021, 132954724, 266337584, 533388643, 1067965265, 2137907009, 4279099869, 8563658486, 17136379382
Offset: 1
For n=3 the a(3)=4 values are the first 1 in the composition 111 and both values in the composition 12 (the compositions 21 and 3 have no fixed points).
- M. Archibald, A. Blecher and A. Knopfmacher, Fixed points in compositions and words, accepted by the Journal of Integer Sequences.
A335713
The sum of the sizes of the largest fixed points over all compositions of n.
Original entry on oeis.org
1, 1, 3, 7, 16, 34, 73, 155, 324, 674, 1393, 2861, 5852, 11929, 24239, 49127, 99360, 200598, 404377, 814135, 1637363, 3290067, 6605980, 13255451, 26583994, 53290694, 106787166, 213919062, 428415074, 857794856, 1717201360, 3437092882, 6878672565, 13764822699
Offset: 1
For n=3 the a(3)=3 values are the first 1 in the composition 111 and the 2 in the composition 12 (the compositions 21 and 3 do not have any fixed points).
- M. Archibald, A. Blecher and A. Knopfmacher, Fixed points in compositions and words, accepted by the Journal of Integer Sequences.
A335712
The sum of the sizes of the minimal fixed points over all compositions of n.
Original entry on oeis.org
1, 1, 2, 6, 12, 27, 54, 115, 237, 486, 997, 2030, 4122, 8350, 16881, 34054, 68609, 138052, 277500, 557328, 1118546, 2243589, 4498004, 9014053, 18058159, 36166338, 72415886, 144970116, 290170091, 580721926, 1162077483, 2325206168, 4652155420, 9307199819
Offset: 1
Example: For n=3 the a(3)=2 values are the first 1s in 111 and 12 (the other compositions 21 and 3 do not have any fixed points).
- M. Archibald, A. Blecher and A. Knopfmacher, Fixed points in compositions and words, accepted by the Journal of Integer Sequences.
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my(N=44,x='x+O('x^N)); Vec( sum(j=1, N, prod(i=1, j-1, (x/(1-x)-x^i) ) *j*x^j * (1-x)/(1-2*x) ) ) \\ Joerg Arndt, Jun 18 2020