The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A341020 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A341020

INVERT transform of the binary weight.
(history; published version)

#13 by Joerg Arndt at Thu Apr 14 03:11:54 EDT 2022

STATUS

reviewed

approved

#12 by Michel Marcus at Thu Apr 14 02:28:57 EDT 2022

STATUS

proposed

reviewed

#11 by Jean-François Alcover at Thu Apr 14 02:23:00 EDT 2022

STATUS

editing

proposed

#10 by Jean-François Alcover at Thu Apr 14 02:22:39 EDT 2022

MATHEMATICA

h[n_] := h[n] = DigitCount[n, 2, 1];

a[n_] := a[n] = If[n == 0, 1,

Sum[a[n - i]*h[i], {i, 1, n}]];

Table[a[n], {n, 0, 36}] (* Jean-François Alcover, Apr 14 2022, after Alois P. Heinz *)

STATUS

approved

editing

#9 by Alois P. Heinz at Tue Feb 02 19:44:31 EST 2021

STATUS

editing

approved

#8 by Alois P. Heinz at Tue Feb 02 19:44:28 EST 2021

LINKS

Alois P. Heinz, <a href="/A341020/b341020.txt">Table of n, a(n) for n = 0..2984</a>

#7 by Alois P. Heinz at Tue Feb 02 19:40:38 EST 2021

COMMENTS

Number of compositions of n into parts where there are A000120(k) sorts of part k.

#6 by Alois P. Heinz at Tue Feb 02 19:38:31 EST 2021

FORMULA

G.f.: 1 / (1 - Sum_{k>=1} A000120(k) * x^k).

#5 by Alois P. Heinz at Tue Feb 02 19:37:33 EST 2021

NAME

0

INVERT transform of the binary weight.

#4 by Alois P. Heinz at Tue Feb 02 17:41:30 EST 2021

MAPLE

h:= proc(n) option remember; add(j, j=Bits[Split](n)) end:

a:= proc(n) option remember; `if`(n=0, 1,

add(a(n-i)*h(i), i=1..n))

end:

seq(a(n), n=0..36);