|
Search: id:A111721
|
|
|
| A111721 |
|
a(n) = a(n-1) + a(n-2) + 5 where a(0) = a(1) = 1. |
|
+0
1
|
|
| 1, 1, 7, 13, 25, 43, 73, 121, 199, 325, 529, 859, 1393, 2257, 3655, 5917, 9577, 15499, 25081, 40585, 65671, 106261, 171937, 278203, 450145, 728353, 1178503, 1906861, 3085369, 4992235, 8077609, 13069849, 21147463, 34217317, 55364785, 89582107
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
a(n+1)/a(n) converges to the golden ratio. - Stefan Steinerberger (hansibal(AT)hotmail.com), Nov 19 2005
|
|
FORMULA
|
for n>1: a(n) = a(n-1) + 6*F(n-1). (a(n)-1)/6 = A000071(n+1) = F(n+1) - 1. Hence a(n) = 6*F(n+1) - 5. - Jonathan Vos Post (jvospost2(AT)yahoo.com), Nov 19 2005
G.f.: (5*x^2-x+1)/(x^3-2*x+1) - Stefan Steinerberger (hansibal(AT)hotmail.com), Nov 19 2005
|
|
EXAMPLE
|
a(2) = a(0) + a(1) + 5 = 1 + 1 + 5 = 7
|
|
PROGRAM
|
(MuPAD): a := 1; b := 1; for n from 1 to 50 do c := a+b+5; print(c); a := b; b := c; end_for; (Steinerberger)
|
|
CROSSREFS
|
Cf. A000045, A000071.
Sequence in context: A137177 A087195 A031887 this_sequence A060455 A072579 A067870
Adjacent sequences: A111718 A111719 A111720 this_sequence A111722 A111723 A111724
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Nov 17 2005
|
|
EXTENSIONS
|
More terms from Stefan Steinerberger (hansibal(AT)hotmail.com), Nov 19 2005
|
|
|
Search completed in 0.002 seconds
|
