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A053197 Number of level partitions of n. 2
1, 1, 2, 2, 4, 3, 6, 5, 10, 8, 13, 12, 21, 18, 27, 27, 42, 38, 54, 54, 77, 76, 101, 104, 143, 142, 183, 192, 249, 256, 323, 340, 432, 448, 550, 585, 722, 760, 918, 982, 1190, 1260, 1502, 1610, 1917, 2048, 2408, 2590, 3053, 3264, 3800, 4097, 4765, 5120, 5910, 6378 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

A partition is level if the powers of 2 dividing its parts are all equal.

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

FORMULA

a(n) = Sum_{k=0..A007814(n)} A000009(n/2^k). a(2*n+1) = A000009(2*n+1) = A078408(n). - Vladeta Jovovic, Sep 29 2004

MAPLE

b:= proc(n, i, p) option remember; `if`(n=0, 1,

     `if`(i<1, 0, add(b(n-i*j, i-p, p), j=0..n/i)))

    end:

a:= n-> (m-> `if`(n=0, 1, add(b(n, (h-> h-1+irem(h, 2)

    )(iquo(n, 2^j))*2^j, 2^(1+j)), j=0..m)))(ilog2(n)):

seq(a(n), n=0..60);  # Alois P. Heinz, Jun 11 2015

MATHEMATICA

a[n_] := Sum[ PartitionsQ[n/2^k], {k, 0, IntegerExponent[n, 2]}]; Table[ a[n], {n, 1, 55}] (* Jean-Fran├žois Alcover, Dec 12 2011, after Vladeta Jovovic *)

CROSSREFS

Cf. A049313, A053195.

Sequence in context: A267451 A062968 A239966 * A088145 A011754 A090105

Adjacent sequences:  A053194 A053195 A053196 * A053198 A053199 A053200

KEYWORD

nonn,nice

AUTHOR

Vladeta Jovovic, Mar 02 2000

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, Jun 11 2015

STATUS

approved

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Last modified December 7 19:05 EST 2016. Contains 278895 sequences.