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A342231 Total sum of parts which are powers of 2 in all partitions of n. 1
0, 1, 4, 6, 17, 24, 43, 64, 115, 159, 247, 347, 513, 704, 1001, 1350, 1894, 2513, 3408, 4489, 5989, 7786, 10226, 13172, 17079, 21800, 27938, 35362, 44900, 56402, 70959, 88545, 110617, 137108, 170051, 209599, 258328, 316685, 388072, 473331, 577026, 700524, 849775, 1027167 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..43.

FORMULA

G.f.: Sum_{k>=0} 2^k*x^(2^k)/(1 - x^(2^k)) / Product_{j>=1} (1 - x^j).

a(n) = Sum_{k=1..n} A038712(k) * A000041(n-k).

EXAMPLE

For n = 4 we have:

------------------------------------

Partitions          Sum of parts

.              which are powers of 2

------------------------------------

4 ..................... 4

3 + 1 ................. 1

2 + 2 ................. 4

2 + 1 + 1 ............. 4

1 + 1 + 1 + 1 ......... 4

------------------------------------

Total ................ 17

So a(4) = 17.

MATHEMATICA

nmax = 43; CoefficientList[Series[Sum[2^k x^(2^k)/(1 - x^(2^k)), {k, 0, Floor[Log[2, nmax]] + 1}]/Product[(1 - x^j), {j, 1, nmax}], {x, 0, nmax}], x]

Table[Sum[(2^IntegerExponent[2 k, 2] - 1) PartitionsP[n - k], {k, 1, n}], {n, 0, 43}]

CROSSREFS

Cf. A000041, A000079, A038712, A066186, A342230.

Sequence in context: A105271 A343758 A024305 * A320245 A337208 A034492

Adjacent sequences:  A342228 A342229 A342230 * A342232 A342233 A342234

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 06 2021

STATUS

approved

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Last modified September 20 02:19 EDT 2021. Contains 347577 sequences. (Running on oeis4.)