|
| |
|
|
A015537
|
|
Expansion of x/(1-5*x-4*x^2).
|
|
12
| |
|
|
0, 1, 5, 29, 165, 941, 5365, 30589, 174405, 994381, 5669525, 32325149, 184303845, 1050819821, 5991314485, 34159851709, 194764516485, 1110461989261, 6331368012245, 36098688018269, 205818912140325, 1173489312774701
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,3
|
|
|
COMMENTS
| First differences give A122690(n) = {1, 4, 24, 136, 776, 4424, 25224, ...}. Partial sums of a(n) are {0, 1, 6, 35, 200, ...} = (A123270(n) - 1)/8. - Alexander Adamchuk, Nov 03 2006
For n>=2, a(n) equals the permanent of the (n-1)X(n-1) tridiagonal matrix with 5's along the main diagonal, and 2's along the superdiagonal and the subdiagonal. [From John M. Campbell, Jul 19 2011]
|
|
|
LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (5,4).
|
|
|
FORMULA
| a(n) = 5*a(n-1) + 4*a(n-2).
a(n)=sum{k=0..floor((n-1)/2), C(n-k-1, k)4^k*5^(n-2k-1)} - Paul Barry, Apr 23 2005
a(n) = sum(k=0..n-1, A122690(k) ). - Alexander Adamchuk, Nov 03 2006
a(n)=(1/41)*sqrt(41)*(((5/2)+(1/2)*sqrt(41))^n-((5/2)-(1/2)*sqrt(41))^n), with n>=0 [From Paolo P. Lava, Jan 13 2009]
|
|
|
MATHEMATICA
| Join[{a=0, b=1}, Table[c=5*b+4*a; a=b; b=c, {n, 100}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 16 2011*)
|
|
|
PROG
| (Sage) [lucas_number1(n, 5, -4) for n in xrange(0, 22)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 24 2009]
|
|
|
CROSSREFS
| Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015535, A015536, A015443, A015447, A030195, A053404, A057087, A083858, A085939, A090017, A091914, A099012, A122690, A123270, A180222, A180226.
Sequence in context: A060926 A098780 A146178 * A141812 A001653 A141814
Adjacent sequences: A015534 A015535 A015536 * A015538 A015539 A015540
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
|
| |
|
|
