The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A343944

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A343944

Total number of parts in all partitions of n into powers of 2: p1 <= p2 <= ... <= p_k such that p_i <= 1 + Sum_{j=1..i-1} p_j.
(history; published version)

#13 by Michael De Vlieger at Wed Nov 16 08:53:08 EST 2022

STATUS

reviewed

approved

#12 by Michel Marcus at Wed Nov 16 08:22:39 EST 2022

STATUS

proposed

reviewed

#11 by Jean-François Alcover at Wed Nov 16 07:18:05 EST 2022

STATUS

editing

proposed

#10 by Jean-François Alcover at Wed Nov 16 07:17:57 EST 2022

MATHEMATICA

b[n_, i_] := b[n, i] = If[n == 0, {1, 0}, If[i < 0, {0, 0}, Function[p, If[p > n || p > n - p + 1, {0, 0}, Function[h, h + {0, h[[1]]}][b[n - p, i]]]][2^i] + b[n, i - 1]]];

a[n_] := b[n, Floor@Log2[n]][[2]];

Table[a[n], {n, 0, 60}] (* Jean-François Alcover, Nov 16 2022, after Alois P. Heinz *)

STATUS

approved

editing

#9 by Alois P. Heinz at Tue May 04 18:39:15 EDT 2021

STATUS

editing

approved

#8 by Alois P. Heinz at Tue May 04 18:38:55 EDT 2021

LINKS

Alois P. Heinz, <a href="/A343944/b343944.txt">Table of n, a(n) for n = 0..20000</a>

#7 by Alois P. Heinz at Tue May 04 18:24:28 EDT 2021

EXAMPLE

a(5) = 12 = 5 + 4 + 3: [1,1,1,1,1], [1,1,1,2], [1,2,2].

a(6) = 15 = 6 + 5 + 4: [1,1,1,1,1,1], [1,1,1,1,2], [1,1,2,2].

a(7) = 29 = 7+6+5+4+4+3: [1,1,1,1,1,1,1], [1,1,1,1,1,2], [1,1,1,2,2], [1,2,2,2], [1,1,1,4], [1,2,4].

#6 by Alois P. Heinz at Tue May 04 18:20:56 EDT 2021

EXAMPLE

a(5) = 12 = 5 + 4 + 3: [1,1,1,1,1], [1,1,1,2], [1,2,2].

#5 by Alois P. Heinz at Tue May 04 18:13:54 EDT 2021

EXAMPLE

a(6) = 15 = 6 + 5 + 4: [1,1,1,1,1,1], [1,1,1,1,2], [1,1,2,2].

#4 by Alois P. Heinz at Tue May 04 18:12:08 EDT 2021

NAME

a

Total number of parts in all partitions of n into powers of 2: p1 <= p2 <= ... <= p_k such that p_i <= 1 + Sum_{j=1..i-1} p_j.