|
| |
|
|
A012814
|
|
Take every 5th term of Padovan sequence A000931.
|
|
2
| |
|
|
0, 1, 5, 21, 86, 351, 1432, 5842, 23833, 97229, 396655, 1618192, 6601569, 26931732, 109870576, 448227521, 1828587033, 7459895657, 30433357674, 124155792775, 506505428836, 2066337330754, 8429820731201
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index to sequences with linear recurrences with constant coefficients, signature (5,-4,1).
|
|
|
FORMULA
| a(n+3) = 5*a(n+2)-4*a(n+1)+a(n).
G.f.: x/(1-5*x+4*x^2-x^3). - Colin Barker, Feb 03 2012
|
|
|
EXAMPLE
| sage: taylor( mul((1-x)/(1-(1-x^2)-(1-x^3)) for i in xrange(1,2)),x,1,22)# solution>> -(x - 1) + 5*(x - 1)^2 - 21*(x - 1)^3 + 86*(x - 1)^4 - 351*(x - 1)^5 +1432*(x - 1)^6 - 5842*(x - 1)^7 + 23833*(x - 1)^8 - 97229*(x - 1)^9 + 396655*(x - 1)^10 - 1618192*(x - 1)^11 +....+ 506505428836*(x - 1)^20 - 2066337330754*(x - 1)^21 + 8429820731201*(x - 1)^22 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 02 2009]
|
|
|
MATHEMATICA
| LinearRecurrence[{5, -4, 1}, {0, 1, 5}, 25] (* Vincenzo Librandi, Feb 03 2012 *)
|
|
|
PROG
| (Other) sage: taylor( mul((1-x)/(1-(1-x^2)-(1-x^3)) for i in xrange(1, 2)), x, 1, 22)# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 02 2009]
(MAGMA) I:=[0, 1, 5 ]; [n le 3 select I[n] else 5*Self(n-1)-4*Self(n-2)+Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 03 2012
|
|
|
CROSSREFS
| a(n) = A012855(n+4)-A012855(n+3).
Sequence in context: A187063 A026855 A097113 * A039919 A010925 A019992
Adjacent sequences: A012811 A012812 A012813 * A012815 A012816 A012817
|
|
|
KEYWORD
| nonn,easy,changed
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| Initial term 0 added by Colin Barker (c.barker(AT)orange.fr), Feb 03 2012
|
| |
|
|
