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A143157 Partial sums of A091512. 4
0, 1, 5, 8, 20, 25, 37, 44, 76, 85, 105, 116, 152, 165, 193, 208, 288, 305, 341, 360, 420, 441, 485, 508, 604, 629, 681, 708, 792, 821, 881, 912, 1104, 1137, 1205, 1240, 1348, 1385, 1461, 1500, 1660, 1701, 1785, 1828, 1960, 2005, 2097, 2144, 2384, 2433, 2533, 2584, 2740, 2793, 2901, 2956, 3180 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..8191

FORMULA

Partial sums of A091512 = Sum {j>=1} j*A001511(j), where A001511 is the ruler sequence.

Row sums of triangle A143156.

a(n) = A249152(2*n)/2 = A249153(n) / 2. - Antti Karttunen, Oct 25 2014

a(n) = Sum_{i=1..2n} floor(i/2)*v_2(i), where v_2(i) = A007814(i) is the exponent of the highest power of 2 dividing i. - Ridouane Oudra, Sep 03 2019

G.f. A(x) satisfies: A(x) = 2*A(x^2)*(1 + x) + x/(1 - x)^3. - Ilya Gutkovskiy, Oct 30 2019

EXAMPLE

a(4) = 20 = sum of row 4 terms of triangle A143156, (7 + 6 + 4 + 3).

a(4) = 20 = partial sums of first 4 terms of A091512: (1 + 4 + 3 + 12).

a(4) = 20 = sum {j=1..4} j*A001511(j) = 1*1 + 2*2 + 3*1 + 4*3).

MATHEMATICA

{0}~Join~Accumulate@ Array[IntegerExponent[(2 #)^#, 2] &, 56] (* Michael De Vlieger, Sep 29 2019 *)

CROSSREFS

Cf. A001511, A007814, A091512, A143156, A249152, A249153.

Sequence in context: A270321 A271885 A295901 * A275236 A270022 A271195

Adjacent sequences:  A143154 A143155 A143156 * A143158 A143159 A143160

KEYWORD

nonn

AUTHOR

Gary W. Adamson, Jul 27 2008

EXTENSIONS

a(0) = 0 prepended and more terms computed by Antti Karttunen, Oct 25 2014

STATUS

approved

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Last modified September 28 13:24 EDT 2020. Contains 337393 sequences. (Running on oeis4.)