|
Search: id:A022100
|
|
|
| A022100 |
|
Fibonacci sequence beginning 1 10. |
|
+0
4
|
|
| 1, 10, 11, 21, 32, 53, 85, 138, 223, 361, 584, 945, 1529, 2474, 4003, 6477, 10480, 16957, 27437, 44394, 71831, 116225, 188056, 304281, 492337, 796618, 1288955, 2085573, 3374528, 5460101, 8834629
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
a(n-1)=sum(P(10;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=9. These are the SW-NE diagonals in P(10;n,k), the (10,1) Pascal triangle A093645. Observation by Paul Barry (pbarry(AT)wit.ie, Apr 29 2004. Proof via recursion relations and comparison of inputs.
|
|
LINKS
|
Tanya Khovanova, Recursive Sequences
|
|
FORMULA
|
a(n)= a(n-1)+a(n-2), n>=2, a(0)=1, a(1)=10. a(-1):=9.
G.f.: (1+9*x)/(1-x-x^2).
a(n)=sum{k=0..n, Fib(n-k+1)(9*binomial(1, k)-8*binomial(0, k))} - Paul Barry (pbarry(AT)wit.ie), May 05 2005
|
|
CROSSREFS
|
a(n) = A109754(9, n+1) = A101220(9, 0, n+1).
Adjacent sequences: A022097 A022098 A022099 this_sequence A022101 A022102 A022103
Sequence in context: A014418 A089591 A064039 this_sequence A041475 A041204 A041202
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
njas
|
|
|
Search completed in 0.002 seconds
|
