|
Search: id:A094585
|
|
|
| A094585 |
|
Triangle T of all positive differences of distinct Fibonacci numbers; also, triangle of all sums of consecutive distinct Fibonacci numbers. |
|
+0
3
|
|
| 1, 2, 3, 3, 5, 6, 5, 8, 10, 11, 8, 13, 16, 18, 19, 13, 21, 26, 29, 31, 32, 21, 34, 42, 47, 50, 52, 53, 34, 55, 68, 76, 81, 84, 86, 87, 55, 89, 110, 123, 131, 136, 139, 141, 142, 89, 144, 178, 199, 212, 220, 225, 228, 230, 231, 144, 233, 288, 322, 343, 356, 364, 369, 372
(list; table; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Row sums = (1,5,14,34,74,...)=A094584. Alternating row sums = (1,1,4,4,12,12,...) given by F(m+1)-1 if m is even and F(m+2)-1 if m is odd. Central numbers = (1,5,16,47,...)=A094586.
|
|
FORMULA
|
T(n, k)=F(n+3)-F(n+3-k)=F(n+1)+F(n)+...+F(n+2-k), for k=1, 2, ..., n; n=1, 2, 3, ...
|
|
EXAMPLE
|
Rows 1 to 5:
1
2 3
3 5 6
5 8 10 11
8 13 16 18 19
T(5,4)=F(8)-F(4)=21-3=18; T(5,4)=F(6)+F(5)+F(4)+F(3)=8+5+3+2=18.
|
|
CROSSREFS
|
Cf. A000045, A094584, A094586.
Sequence in context: A023156 A051599 A064464 this_sequence A003967 A099209 A099208
Adjacent sequences: A094582 A094583 A094584 this_sequence A094586 A094587 A094588
|
|
KEYWORD
|
nonn,tabl
|
|
AUTHOR
|
Clark Kimberling (ck6(AT)evansville.edu), May 13 2004
|
|
|
Search completed in 0.002 seconds
|
