|
Search: id:A138112
|
|
|
| A138112 |
|
a(n)=3a(n-1)-4a(n-2)+2a(n-3)-a(n-4), a(0)=a(1)=a(2)=0, a(3)=1, a(4)=3. |
|
+0
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
(list; graph; listen)
|
|
|
OFFSET
|
0,5
|
|
|
COMMENT
|
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 1st 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 (mathar(AT)strw.leidenuniv.nl), Jul 04 2008
|
|
FORMULA
|
O.g.f.: x^3/(1-3x+4x^2-2x^3+x^4). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 04 2008
|
|
CROSSREFS
|
Cf. A138003, A103311, A105371.
Sequence in context: A133758 A021742 A152416 this_sequence A106233 A077860 A078063
Adjacent sequences: A138109 A138110 A138111 this_sequence A138113 A138114 A138115
|
|
KEYWORD
|
sign
|
|
AUTHOR
|
Paul Curtz (bpcrtz(AT)free.fr), May 04 2008
|
|
EXTENSIONS
|
Edited and extended by R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 04 2008
|
|
|
Search completed in 0.002 seconds
|
