|
Search: id:A015537
|
|
|
| A015537 |
|
Linear 2nd order recurrence. |
|
+0
4
|
|
| 0, 1, 5, 29, 165, 941, 5365, 30589, 174405, 994381, 5669525, 32325149, 184303845, 1050819821, 5991314485, 34159851709, 194764516485, 1110461989261, 6331368012245, 36098688018269, 205818912140325, 1173489312774701
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
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 (alex(AT)kolmogorov.com), Nov 03 2006
|
|
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 (pbarry(AT)wit.ie), Apr 23 2005
a(n) = Sum[ A122690(k), {k,0,n-1} ] for n>0. - Alexander Adamchuk (alex(AT)kolmogorov.com), 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 (ppl(AT)spl.at), Jan 13 2009]
|
|
PROGRAM
|
(Other) sage: [lucas_number1(n, 5, -4) for n in xrange(0, 22)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 24 2009]
|
|
CROSSREFS
|
Cf. A122690, A123270.
Sequence in context: A060926 A098780 A146178 this_sequence A141812 A001653 A141814
Adjacent sequences: A015534 A015535 A015536 this_sequence A015538 A015539 A015540
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
Olivier Gerard (olivier.gerard(AT)gmail.com)
|
|
|
Search completed in 0.002 seconds
|
