A147657 -id:A147657 - cp's OEIS frontend

A147658 (1, 2, -4, 6, -8, ...) interleaved with (3, -3, 3, -3, 3, ...).

1, 3, 2, -3, -4, 3, 6, -3, -8, 3, 10, -3, -12, 3, 14, -3, -16, 3, 18, -3, -20, 3, 22, -3, -24, 3, 26, -3, -28, 3, 30, -3, -32, 3, 34, -3, -36, 3, 38, -3, -40, 3, 42, -3, -44, 3, 46, -3, -48, 3, 50, -3, -52, 3, 54, -3, -56, 3, 58, -3, -60, 3, 62, -3, -64

Offset: 1

Gary W. Adamson, Nov 09 2008

POLYMOTZKINT A147657 = [1,2,3,...].
POLYMOTZKINTINV operation on [1,3,5,7,...], such that POLYMOTZKINT A147658 = [1,3,5,7,...].
Cf. A005717 for an example of the POLYMOTZKINT operation.

Index entries for linear recurrences with constant coefficients, signature (0,-2,0,-1).

Cf. A005717, A147657.

with(ListTools): Flatten([1, seq([(-1)^(k-1)*3, (-1)^(k-1)*2*k], k=1..32)]); # Georg Fischer, Nov 02 2021

a(1) = 1; a(2*k) = (-1)^(k-1)*3; a(2*k+1) = (-1)^(k-1)*2*k for k >= 1. - Georg Fischer, Nov 02 2021

a(25) ff. corrected by Georg Fischer, Nov 02 2021

A174007 a(2n+1)=2. a(2n)= 1-n.

Original entry on oeis.org

2, 0, 2, -1, 2, -2, 2, -3, 2, -4, 2, -5, 2, -6, 2, -7, 2, -8, 2, -9, 2, -10, 2, -11, 2, -12, 2, -13, 2, -14, 2, -15, 2, -16, 2, -17, 2, -18, 2, -19, 2, -20, 2, -21, 2, -22, 2, -23, 2, -24, 2, -25, 2, -26, 2, -27, 2, -28, 2, -29, 2, -30, 2, -31, 2, -32, 2, -33, 2, -34, 2, -35, 2

Offset: 1

Paul Curtz, Mar 05 2010

A064680(n)+A022998(n-1) =c(n) = 2, 2, 10, 5, 18, 8, 26, 11,.. has differences c(2n)-c(2n-1) = -5*(n-1) = -A008587(n-1).

Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).

Cf. A147657.

a(n) = n/4+3/2-(-1)^n*(n/4+1/2).
a(n)= +2*a(n-2) -a(n-4). G.f.: -x*(-2+2*x^2+x^3) / ( (x-1)^2*(1+x)^2 ).
a(n+1)-a(n) = (-1)^n*A008619(n+1).
a(n) = A064680(n)-A022998(n-1).

cp's OEIS Frontend

A147658 (1, 2, -4, 6, -8, ...) interleaved with (3, -3, 3, -3, 3, ...).

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