|
Search: id:A085939
|
|
|
| A085939 |
|
Horadam sequence (0,1,6,4). |
|
+0
5
|
|
| 0, 1, 4, 22, 112, 580, 2992, 15448, 79744, 411664, 2125120, 10970464, 56632576, 292353088, 1509207808, 7790949760, 40219045888, 207621882112, 1071801803776, 5532938507776, 28562564853760
(list; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
a(n) / a(n-1) converges to 10^1/2 + 2 as n approaches infinity. 10^1/2 + 2 can also be written as 2^1/2 * (2^1/2 + 5^1/2), ((2 * 2^1/2) * Phi) - 2^1/2 + 2, and 2^1/2 * (2^1/2 + (L(n) / F(n))), where L(n) is the n-th Lucas number and F(n) is the n-th Fibonacci number as n approaches infinity.
|
|
LINKS
|
Eric Weisstein, Lucas Number
Eric Weisstein, Lucas Sequence
Eric Weisstein, Horadam Sequence
Eric Weisstein, Fibonacci Number
Eric Weisstein, Pell Number
|
|
FORMULA
|
a(n) = s*a(n-1) + r*a(n-2); for n > 1, where a(0) = 0, a(1) = 1, s = 4, r = 6
|
|
EXAMPLE
|
a(4) = 112 because a(3) = 22, a(2) = 4, s = 4, r = 6 and (4 * 22) + (6 * 4) = 112.
|
|
CROSSREFS
|
Cf. A024318, A000032, A000129.
Adjacent sequences: A085936 A085937 A085938 this_sequence A085940 A085941 A085942
Sequence in context: A144047 A077543 A084157 this_sequence A106835 A025569 A098834
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
Ross La Haye (rlahaye(AT)new.rr.com), Aug 16 2003
|
|
|
Search completed in 0.002 seconds
|
