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 A242628 Irregular table enumerating partitions; n-th row has partitions in previous row with each part incremented, followed by partitions in previous row with an additional part of size 1. 5
 1, 2, 1, 1, 3, 2, 2, 2, 1, 1, 1, 1, 4, 3, 3, 3, 2, 2, 2, 2, 3, 1, 2, 2, 1, 2, 1, 1, 1, 1, 1, 1, 5, 4, 4, 4, 3, 3, 3, 3, 4, 2, 3, 3, 2, 3, 2, 2, 2, 2, 2, 2, 4, 1, 3, 3, 1, 3, 2, 1, 2, 2, 2, 1, 3, 1, 1, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 6, 5, 5, 5, 4, 4, 4, 4, 5, 3, 4, 4, 3, 4, 3, 3, 3, 3, 3, 3, 5, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This can be calculated using the binary expansion of n; see the PARI program. The n-th row consists of all partitions with hook size (maximum + number of parts - 1) equal to n. The partitions in row n of this sequence are the conjugates of the partitions in row n of A125106 taken in reverse order. LINKS Alois P. Heinz, Rows n = 1..12, flattened EXAMPLE The table starts:   1;   2; 1,1;   3; 2,2; 2,1; 1,1,1;   4; 3,3; 3,2; 2,2,2; 3,1 2,2,1 2,1,1 1,1,1,1;   ... MAPLE b:= proc(n) option remember; `if`(n=1, [[1]],       [map(x-> map(y-> y+1, x), b(n-1))[],        map(x-> [x[], 1], b(n-1))[]])     end: T:= n-> map(x-> x[], b(n))[]: seq(T(n), n=1..7);  # Alois P. Heinz, Sep 25 2015 MATHEMATICA T[1] = {{1}}; T[n_] := T[n] = Join[T[n-1]+1, Append[#, 1]& /@ T[n-1]]; Array[T, 7] // Flatten (* Jean-François Alcover, Jan 25 2021 *) PROG (PARI) apart(n) = local(r=[1]); while(n>1, if(n%2==0, for(k=1, #r, r[k]++), r=concat(r, [1])); n\=2); r \\ Generates n-th partition. CROSSREFS Cf. A241596 (another version of this list of partitions), A125106, A240837, A112531, A241597 (compositions). For other schemes to list integer partitions, please see for example A227739, A112798, A241918, A114994. Sequence in context: A208101 A131333 A120643 * A111867 A326036 A133776 Adjacent sequences:  A242625 A242626 A242627 * A242629 A242630 A242631 KEYWORD nonn,tabf AUTHOR Franklin T. Adams-Watters, May 19 2014 STATUS approved

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Last modified September 26 12:36 EDT 2021. Contains 347665 sequences. (Running on oeis4.)