A092532 - OEIS

%I #22 Sep 08 2022 08:45:13

%S 1,1,1,1,2,2,2,2,4,4,4,4,6,6,6,6,9,9,9,9,12,12,12,12,16,16,16,16,20,

%T 20,20,20,25,25,25,25,30,30,30,30,36,36,36,36,42,42,42,42,49,49,49,49,

%U 56,56,56,56,64,64,64,64,72,72,72,72,81,81,81,81,90,90,90,90,100,100,100,100

%N G.f.: 1/((1-x)*(1-x^4)*(1-x^8)).

%C Number of partitions of n into parts 1, 4, and 8. - _Joerg Arndt_, Aug 10 2014

%H Vincenzo Librandi, <a href="/A092532/b092532.txt">Table of n, a(n) for n = 0..1000</a>

%H G. Nebe, E. M. Rains and N. J. A. Sloane, <a href="http://neilsloane.com/doc/cliff2.html">Self-Dual Codes and Invariant Theory</a>, Springer, Berlin, 2006.

%H <a href="/index/Mo#Molien">Index entries for Molien series</a>

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 0, 1, -1, 0, 0, 1, -1, 0, 0, -1, 1).

%F a(0)=1, a(1)=1, a(2)=1, a(3)=1, a(4)=2, a(5)=2, a(6)=2, a(7)=2, a(8)=4, a(9)=4, a(10)=4, a(11)=4, a(12)=6; for n>12, a(n)=a(n-1)+a(n-4)-a(n-5)+a(n-8)- a(n-9)- a(n-12)+a (n-13). - _Harvey P. Dale_, Aug 10 2014

%t CoefficientList[Series[1/((1-x)(1-x^4)(1-x^8)),{x,0,80}],x] (* or *) LinearRecurrence[{1,0,0,1,-1,0,0,1,-1,0,0,-1,1},{1,1,1,1,2,2,2,2,4,4,4,4,6},80] (* _Harvey P. Dale_, Aug 10 2014 *)

%o (Magma) [n le 13 select Floor(Floor(1+(n+3)/4)^2/4) else Self(n-1)+Self(n-4)-Self(n-5)+Self(n-8)-Self(n-9)-Self(n-12)+Self(n-13): n in [1..100]]; // _Vincenzo Librandi_, Aug 10 2014

%K nonn,easy

%O 0,5

%A _N. J. A. Sloane_, Apr 08 2004