OFFSET
0,3
COMMENTS
a(n) appears on row 1 of the array illustrated in A066099.
Except for initial zero, ordinal transform of A062050. After initial zero, n-th chunk consists of n, one n-1, two (n-2)'s, ..., 2^(k-1) (n-k)'s, ..., 2^(n-1) 1's. - Franklin T. Adams-Watters, Sep 11 2006
Zero together with a triangle read by rows in which row j lists the first 2^(j-1) terms of A001511 in nonincreasing order, j >= 1, see example. Also row j lists the first parts, in nonincreasing order, of the compositions of j. - Omar E. Pol, Sep 11 2013
The n-th row represents the frequency distribution of 1, 2, 3, ..., 2^(n-1) in the first 2^n - 1 terms of A003602. - Gary W. Adamson, Jun 10 2021
FORMULA
From Daniel Starodubtsev, Aug 05 2021: (Start)
a(2n+1) = a(n), a(2n) = a(n) + A036987(n-1) for n > 1 with a(0) = 0, a(1) = 1. (End)
EXAMPLE
From Omar E. Pol, Aug 30 2013: (Start)
Written as an irregular triangle with row lengths A011782:
0;
1;
2,1;
3,2,1,1;
4,3,2,2,1,1,1,1;
5,4,3,3,2,2,2,2,1,1,1,1,1,1,1,1;
6,5,4,4,3,3,3,3,2,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1;
...
(End)
MATHEMATICA
nmax = 105;
A062050 = Flatten[Table[Range[2^n], {n, 0, Log[2, nmax] // Ceiling}]];
Module[{b}, b[_] = 0;
a[n_] := If[n == 0, 0, With[{t = A062050[[n]]}, b[t] = b[t] + 1]]];
a /@ Range[0, nmax] (* Jean-François Alcover, Jan 12 2022 *)
PROG
(PARI) lista(nn) = {my(v = vector(nn)); v[1] = 1; for (i=2, nn, v[i] = mg(i-1)*v[(i+1)\2]; ); for (i=1, nn, print1(valuation(v[i], 2), ", "); ); } \\ Michel Marcus, Feb 09 2014
(PARI) my(L(n)=if(n, logint(n, 2), -1)); a(n) = my(p=L(n)); p - L(n-1<<p); \\ Kevin Ryde, Aug 06 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Alford Arnold, Nov 12 2001
EXTENSIONS
More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 29 2003
STATUS
approved