A189887 Dimension of homogeneous component of degree n in x in the Malcev-Poisson superalgebra S^tilde(M).

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

Offset: 1

Author

N. J. A. Sloane, Apr 29 2011

Keywords

• nonn
• easy

Links

• Paolo Xausa, Table of n, a(n) for n = 1..10000
• Ivan Shestakov and Natalia Zhukavets, The Malcev Poisson superalgebra of the free Malcev superalgebra on one odd generator, J. Algebra Appl. 5 (2006), 521-535.
• Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

Crossrefs

Apart from initial terms, same as A047415.

Programs

Maple

f:=proc(n) local k,r;
if n <= 2 then 1 elif n=3 then 2
else k:=floor(n/4); r:=n-4*k;
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;
fi;
end;

Mathematica

LinearRecurrence[{2, -2, 2, -1}, {1, 1, 2, 3, 4, 6, 9}, 100] (* Paolo Xausa, Jun 26 2024 *)

Formula

See Maple code.

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