A000749 -id:A000749 - cp's OEIS frontend

A138569 First differences of A137776.

0, 1, 0, 1, 0, 1, 1, 0, 4, -2, 10, -4, 20, -4, 36, 0, 64, 8, 120, 16, 240, 16, 496, 0, 1024, -32, 2080, -64, 4160, -64, 8256, 0, 16384, 128, 32640, 256, 65280, 256, 130816, 0, 262144, -512, 524800, -1024, 1049600, -1024, 2098176, 0, 4194304, 2048, 8386560, 4096, 16773120

Offset: 0

Paul Curtz, May 12 2008

sign

Index entries for linear recurrences with constant coefficients, signature (0, 4, 0, -6, 0, 4).

Cf. A135356.

a(n)=4a(n-2)-6a(n-4)+4a(n-6), n>7.
a(2n)=A000749(n). a(2n+1)=(-1)^(n+1)*A009116(n-1), n>0.
O.g.f.: x(1-x)(x^4-2x^2+1+x-2x^3+2x^5)/((1-2x^2)(1-2x^2+2x^4)). - R. J. Mathar, Aug 02 2008

Edited and extended by R. J. Mathar, Aug 02 2008

A161909 Inverse binomial transform of A181586.

Original entry on oeis.org

0, 0, 1, -3, 7, -13, 23, -41, 79, -161, 335, -689, 1391, -2769, 5487, -10897, 21743, -43537, 87279, -174865, 349935, -699665, 1398511, -2795793, 5590767, -11182353, 22367983, -44740881, 89485039, -178966801, 357920495, -715821329, 1431629551, -2863272209, 5726596847

Offset: 0

Paul Curtz, Jan 31 2011

A181586(n) and successive differences:
   0,  0,  1,  0,   1,  2,
   0,  1, -1,  1,   1,  3,
   1, -2,  2,  0,   2,  0,
  -3,  4, -2,  2,  -2,  6,
   7, -6,  4, -4,   8, -4,
-13, 10, -8, 12, -12, 12.
First column is a(n).

Index entries for linear recurrences with constant coefficients, signature (-3,-2,2,4).

a(n+2)=( (2*a(n)+A077950(n)) signed)
a(n)-a(n-1) = (-1)^n*A000749(n+2).
G.f. -x^2 / ( (x-1)*(2*x+1)*(2*x^2+2*x+1) ). - R. J. Mathar, Feb 06 2011

cp's OEIS Frontend

A138569 First differences of A137776.

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