OFFSET
0,5
COMMENTS
Obeys also the recurrence a(n)=5a(n-1)-10a(n-2)+10a(n-3)-5a(n-4)+2a(n-5), so the sequence is identical to its fifth differences (cf. A135356). a(n) = A138110(0,n): if A138110 is interpreted as an array with five rows, this is the top row.
The first differences are represented by A100334(n-1).
The 2nd differences are represented by A103311(n).
The 3rd differences are essentially represented by -A138003(n-2).
The 4th differences are represented by -A105371(n).
A102312 contains the absolute values of the terms which occur in pairs, for example a(5)=a(6)=5=A102312(1), a(10)=a(11)= -55 = -A102312(2).
Inverse BINOMIAL transform yields two zeros followed by A105384. - R. J. Mathar, Jul 04 2008
LINKS
Index entries for linear recurrences with constant coefficients, signature (3, -4, 2, -1).
FORMULA
O.g.f.: x^3/(1-3x+4x^2-2x^3+x^4). - R. J. Mathar, Jul 04 2008
MATHEMATICA
CoefficientList[Series[x^3/(1-3x+4x^2-2x^3+x^4), {x, 0, 45}], x] (* or *) LinearRecurrence[{3, -4, 2, -1}, {0, 0, 0, 1}, 45] (* Harvey P. Dale, Jun 22 2011 *)
CROSSREFS
KEYWORD
sign
AUTHOR
Paul Curtz, May 04 2008
EXTENSIONS
Edited and extended by R. J. Mathar, Jul 04 2008
STATUS
approved