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A301896 a(n) = product of total number of 0's and total number of 1's in binary expansions of 0, ..., n. 1
0, 1, 4, 8, 20, 35, 54, 72, 117, 165, 221, 280, 352, 425, 504, 576, 726, 875, 1036, 1200, 1386, 1575, 1776, 1976, 2214, 2451, 2700, 2944, 3216, 3479, 3750, 4000, 4455, 4897, 5355, 5808, 6300, 6789, 7296, 7800, 8364, 8925, 9504, 10080, 10695, 11305, 11931, 12544, 13260, 13965, 14688 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..50.

Index entries for sequences related to binary expansion of n

FORMULA

a(n) = A059015(n)*A000788(n).

a(2^k-1) = 2^(k-2)*(2^k*(k - 2) + 4)*k.

EXAMPLE

+---+-----+---+---+---+---+----------+

| n | bin.|0's|sum|1's|sum|   a(n)   |

+---+-----+---+---+---+---+----------+

| 0 |   0 | 1 | 1 | 0 | 0 | 1*0 =  0 |

| 1 |   1 | 0 | 1 | 1 | 1 | 1*1 =  1 |

| 2 |  10 | 1 | 2 | 1 | 2 | 2*2 =  4 |

| 3 |  11 | 0 | 2 | 2 | 4 | 2*4 =  8 |

| 4 | 100 | 2 | 4 | 1 | 5 | 4*5 = 20 |

| 5 | 101 | 1 | 5 | 2 | 7 | 5*7 = 35 |

| 6 | 110 | 1 | 6 | 2 | 9 | 6*9 = 54 |

+---+-----+---+---+---+---+----------+

bin. - n written in base 2;

0's - number of 0's in binary expansion of n;

1's - number of 1's in binary expansion of n;

sum - total number of 0's (or 1's) in binary expansions of 0, ..., n.

MATHEMATICA

Accumulate[DigitCount[Range[0, 50], 2, 0]] Accumulate[DigitCount[Range[0, 50], 2, 1]]

CROSSREFS

Cf. A000120, A000788, A023416, A059015, A071295, A301336.

Sequence in context: A047185 A034733 A152233 * A053303 A097164 A133628

Adjacent sequences:  A301893 A301894 A301895 * A301897 A301898 A301899

KEYWORD

nonn,base

AUTHOR

Ilya Gutkovskiy, Mar 28 2018

STATUS

approved

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Last modified June 13 05:33 EDT 2021. Contains 344981 sequences. (Running on oeis4.)