A189887 - OEIS

%I #23 Jun 26 2024 04:26:04

%S 1,1,2,3,4,6,9,11,12,14,17,19,20,22,25,27,28,30,33,35,36,38,41,43,44,

%T 46,49,51,52,54,57,59,60,62,65,67,68,70,73,75,76,78,81,83,84,86,89,91,

%U 92,94,97,99,100,102,105,107,108,110,113,115,116,118,121,123,124,126,129,131,132,134,137,139,140,142,145,147,148,150,153,155

%N Dimension of homogeneous component of degree n in x in the Malcev-Poisson superalgebra S^tilde(M).

%H Paolo Xausa, <a href="/A189887/b189887.txt">Table of n, a(n) for n = 1..10000</a>

%H Ivan Shestakov and Natalia Zhukavets, <a href="https://doi.org/10.1142/S0219498806001867">The Malcev Poisson superalgebra of the free Malcev superalgebra on one odd generator</a>, J. Algebra Appl. 5 (2006), 521-535.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2,-1).

%F See Maple code.

%F a(n) = (1/4+i/4)*((-11+11*i)-i*(-i)^n+i^n)+2*n for n>3, where i=sqrt(-1). a(n) = 2*a(n-1)-2*a(n-2)+2*a(n-3)-a(n-4) for n>7. G.f.: x*(x^6+x^5+x^4-x^3+2*x^2-x+1) / ((x-1)^2*(x^2+1)). - _Colin Barker_, Jul 24 2013

%p f:=proc(n) local k,r;

%p if n <= 2 then 1 elif n=3 then 2

%p else k:=floor(n/4); r:=n-4*k;

%p if r=0 then 8*k-5 elif r=1 then 8*k-4 elif r=2 then 8*k-2 else 8*k+1; fi;

%p fi;

%p end;

%t LinearRecurrence[{2, -2, 2, -1}, {1, 1, 2, 3, 4, 6, 9}, 100] (* _Paolo Xausa_, Jun 26 2024 *)

%Y Apart from initial terms, same as A047415.

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_, Apr 29 2011