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A306903 Sum over all partitions of n of the bitwise XOR of the parts. 6
0, 1, 2, 7, 8, 19, 26, 61, 70, 126, 146, 270, 308, 519, 604, 1054, 1222, 1929, 2208, 3454, 3930, 5862, 6576, 9833, 11102, 16052, 17904, 25752, 28764, 40479, 44830, 62988, 70188, 97151, 107662, 148141, 164710, 223783, 247380, 334035, 370406, 495313, 547000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Wikipedia, Bitwise operation

Wikipedia, Commutative property

Wikipedia, Identity element

Wikipedia, Partition (number theory)

Wikipedia, Truth table

FORMULA

a(n) is odd <=> n in { A067567 }.

MAPLE

b:= proc(n, i, r) option remember; `if`(i<1, 0, (t->

      `if`(i<n, b(n-i, min(i, n-i), t), 0)+

      `if`(i=n, t, 0)+b(n, i-1, r))(Bits[Xor](i, r)))

    end:

a:= n-> b(n$2, 0):

seq(a(n), n=0..45);

CROSSREFS

Cf. A006906, A066186, A067567, A306884, A306895, A306901, A306902, A306925.

Sequence in context: A101518 A055247 A015617 * A026579 A167767 A054601

Adjacent sequences:  A306900 A306901 A306902 * A306904 A306905 A306906

KEYWORD

nonn,base

AUTHOR

Alois P. Heinz, Mar 15 2019

STATUS

approved

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Last modified June 22 20:38 EDT 2021. Contains 345389 sequences. (Running on oeis4.)