A047415 -id:A047415 - cp's OEIS frontend

A047481 Numbers that are congruent to {0, 2, 5, 7} mod 8.

0, 2, 5, 7, 8, 10, 13, 15, 16, 18, 21, 23, 24, 26, 29, 31, 32, 34, 37, 39, 40, 42, 45, 47, 48, 50, 53, 55, 56, 58, 61, 63, 64, 66, 69, 71, 72, 74, 77, 79, 80, 82, 85, 87, 88, 90, 93, 95, 96, 98, 101, 103, 104, 106, 109, 111, 112, 114, 117, 119, 120, 122, 125

Offset: 1

N. J. A. Sloane

Complement of A047415.

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (2,-2,2,-1).

Cf. A047415, A047524, A047615.

I:=[0, 2, 5, 7, 8]; [n le 5 select I[n] else Self(n-1)+Self(n-4)-Self(n-5): n in [1..70]]; // Vincenzo Librandi, May 16 2012

A047481:=n->(-1*((-1)^((n-1)/2-(-1)^n/4-1/4)))/2+2*(n-1)+1/2: seq(A047481(n), n=1..100); # Wesley Ivan Hurt, Jun 01 2016

Select[Range[0,300], MemberQ[{0,2,5,7}, Mod[#,8]]&] (* Vincenzo Librandi, May 16 2012 *)
LinearRecurrence[{2,-2,2,-1},{0,2,5,7},70] (* Harvey P. Dale, May 28 2017 *)

a(n)=[-1,0,2,5][n%4]+n\4*8 \\ Charles R Greathouse IV, Mar 05 2014

x='x+O('x^100); concat(0, Vec(x^2*(2+x+x^2)/((1-x)^2*(1+x^2)))) \\ Altug Alkan, Dec 24 2015

From Colin Barker, May 14 2012: (Start)
a(n) = (1/4+i/4)*((-3+3*i)-i*(-i)^n+i^n+(4-4*i)*n) where i=sqrt(-1).
G.f.: x^2*(2+x+x^2)/((1-x)^2*(1+x^2)). (End)
a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - a(n-4) for n>4. - Vincenzo Librandi, May 16 2012
a(n) = (-1*((-1)^((n-1)/2-(-1)^n/4-1/4)))/2+2*(n-1)+1/2.
a(n) = cos(n*Pi/2)-1/2*cos((n-1)*Pi/2)-1/2*cos(n*Pi/2)+2*(n-1)+1/2. - Cédric Christian Bernard Gagneux, Mar 05 2014
a(2k) = A047524, a(2k-1) = A047615(k). - Wesley Ivan Hurt, Jun 01 2016
E.g.f.: (2 - sin(x) + cos(x) + (4*x - 3)*exp(x))/2. - Ilya Gutkovskiy, Jun 02 2016
Sum_{n>=2} (-1)^n/a(n) = (3-sqrt(2))*log(2)/8 + sqrt(2)*log(2+sqrt(2))/4 - Pi/16. - Amiram Eldar, Dec 21 2021

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

Original entry on oeis.org

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

N. J. A. Sloane, Apr 29 2011

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).

Apart from initial terms, same as A047415.

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;

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

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

cp's OEIS Frontend

A047481 Numbers that are congruent to {0, 2, 5, 7} mod 8.

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