login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A087787 a(n) = Sum_{k=0..n} (-1)^(n-k)*A000041(k). 13

%I #28 Oct 25 2023 14:59:00

%S 1,0,2,1,4,3,8,7,15,15,27,29,48,53,82,94,137,160,225,265,362,430,572,

%T 683,892,1066,1370,1640,2078,2487,3117,3725,4624,5519,6791,8092,9885,

%U 11752,14263,16922,20416,24167,29007,34254,40921,48213,57345,67409

%N a(n) = Sum_{k=0..n} (-1)^(n-k)*A000041(k).

%C Essentially first differences of A024786 (see the formula). Also, a(n) is the number of 2's in the last section of the set of partitions of n+2 (see A135010). - _Omar E. Pol_, Sep 10 2008

%H Vaclav Kotesovec, <a href="/A087787/b087787.txt">Table of n, a(n) for n = 0..10000</a>

%F G.f.: 1/(1+x)*1/Product_{k>0} (1-x^k).

%F a(n) = 1/n*Sum_{k=1..n} (sigma(k)+(-1)^k)*a(n-k).

%F a(n) = A024786(n+2)-A024786(n+1). - _Omar E. Pol_, Sep 10 2008

%F a(n) ~ exp(Pi*sqrt(2*n/3)) / (8*sqrt(3)*n) * (1 + (11*Pi/(24*sqrt(6)) - sqrt(3/2)/Pi)/sqrt(n) - (11/16 + (23*Pi^2)/6912)/n). - _Vaclav Kotesovec_, Nov 05 2016

%F a(n) = A000041(n) - a(n-1). - _Jon Maiga_, Aug 29 2019

%t Table[Sum[(-1)^(n-k)*PartitionsP[k], {k,0,n}], {n,0,50}] (* _Vaclav Kotesovec_, Aug 16 2015 *)

%t (* more efficient program *) sig = 1; su = 1; Flatten[{1, Table[sig = -sig; su = su + sig*PartitionsP[n]; Abs[su], {n, 1, 50}]}] (* _Vaclav Kotesovec_, Nov 06 2016 *)

%o (Python)

%o from sympy import npartitions

%o def A087787(n): return sum(-npartitions(k) if n-k&1 else npartitions(k) for k in range(n+1)) # _Chai Wah Wu_, Oct 25 2023

%Y Cf. A000041, A024786, A135010, A138121, A141285.

%K nonn

%O 0,3

%A _Vladeta Jovovic_, Oct 07 2003

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 11:59 EDT 2024. Contains 371254 sequences. (Running on oeis4.)