|
| |
|
|
A022393
|
|
Fibonacci sequence beginning 1 23.
|
|
0
| |
|
|
1, 23, 24, 47, 71, 118, 189, 307, 496, 803, 1299, 2102, 3401, 5503, 8904, 14407, 23311, 37718, 61029, 98747, 159776, 258523, 418299, 676822, 1095121, 1771943, 2867064, 4639007, 7506071, 12145078
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| a(n-1)=sum(P(23;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=22. These are the SW-NE diagonals in P(23;n,k), the (23,1) Pascal triangle. Cf. A093645 for the (10,1) Pascal triangle. 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)=23. a(-1):=22.
G.f.: (1+22*x)/(1-x-x^2).
|
|
|
MATHEMATICA
| a={}; b=1; c=23; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 4!}]; a [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 18 2008]
a[1]=1; a[2]=23; a[n_]:=a[n]=a[n - 1]+a[n - 2] [From J.M. Grau Ribas (grau(AT)telecable.es), Feb 15 2010]
LinearRecurrence[{1, 1}, {1, 23}, 30] (* From Harvey P. Dale, Sep 30 2011 *)
|
|
|
CROSSREFS
| Sequence in context: A007638 A031332 A122470 * A042068 A042066 A042070
Adjacent sequences: A022390 A022391 A022392 * A022394 A022395 A022396
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
