|
Search: id:A022391
|
|
|
| A022391 |
|
Fibonacci sequence beginning 1 21. |
|
+0
1
|
|
| 1, 21, 22, 43, 65, 108, 173, 281, 454, 735, 1189, 1924, 3113, 5037, 8150, 13187, 21337, 34524, 55861, 90385, 146246, 236631, 382877, 619508, 1002385, 1621893, 2624278, 4246171, 6870449, 11116620
(list; graph; listen)
|
|
|
OFFSET
|
0,2
|
|
|
COMMENT
|
a(n-1)=sum(P(21;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=20. These are the SW-NE diagonals in P(21;n,k), the (21,1) 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
S. Kak, The Golden Mean and the Physics of Aesthetics
|
|
FORMULA
|
a(n)= a(n-1)+a(n-2), n>=2, a(0)=1, a(1)=21. a(-1):=20.
G.f.: (1+20*x)/(1-x-x^2).
|
|
MATHEMATICA
|
a={}; b=1; c=21; 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]
|
|
CROSSREFS
|
Sequence in context: A141439 A125737 A160782 this_sequence A041890 A041892 A041894
Adjacent sequences: A022388 A022389 A022390 this_sequence A022392 A022393 A022394
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
Search completed in 0.002 seconds
|
