

A138112


a(n)=3a(n1)4a(n2)+2a(n3)a(n4), a(0)=a(1)=a(2)=0, a(3)=1, a(4)=3.


5



0, 0, 0, 1, 3, 5, 5, 0, 13, 34, 55, 55, 0, 144, 377, 610, 610, 0, 1597, 4181, 6765, 6765, 0, 17711, 46368, 75025, 75025, 0, 196418, 514229, 832040, 832040, 0, 2178309, 5702887, 9227465, 9227465, 0, 24157817, 63245986, 102334155, 102334155
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OFFSET

0,5


COMMENTS

Obeys also the recurrence a(n)=5a(n1)10a(n2)+10a(n3)5a(n4)+2a(n5), 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(n1).
The 2nd differences are represented by A103311(n).
The 3rd differences are essentially represented by A138003(n2).
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

Table of n, a(n) for n=0..41.
Index entries for linear recurrences with constant coefficients, signature (3, 4, 2, 1).


FORMULA

O.g.f.: x^3/(13x+4x^22x^3+x^4).  R. J. Mathar, Jul 04 2008


MATHEMATICA

CoefficientList[Series[x^3/(13x+4x^22x^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

Cf. A138003, A103311, A105371.
Sequence in context: A284867 A152416 A200334 * A106233 A198492 A077860
Adjacent sequences: A138109 A138110 A138111 * A138113 A138114 A138115


KEYWORD

sign


AUTHOR

Paul Curtz, May 04 2008


EXTENSIONS

Edited and extended by R. J. Mathar, Jul 04 2008


STATUS

approved



