|
| |
|
|
A022097
|
|
Fibonacci sequence beginning 1 7.
|
|
12
| |
|
|
1, 7, 8, 15, 23, 38, 61, 99, 160, 259, 419, 678, 1097, 1775, 2872, 4647, 7519, 12166, 19685, 31851, 51536, 83387, 134923, 218310, 353233, 571543, 924776, 1496319, 2421095, 3917414, 6338509, 10255923, 16594432, 26850355, 43444787, 70295142, 113739929
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 0,2
|
|
|
COMMENTS
| a(n-1)=sum(P(7;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=6. These are the SW-NE diagonals in P(7;n,k), the (7,1) Pascal triangle A093564. 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)=7. a(-1):=6.
G.f.: (1+6*x)/(1-x-x^2).
Row sums of triangle A131778 starting (1, 7, 8, 15, 23, 38,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 14 2007
a(n)= (2^(-1-n) ((1-Sqrt[5])^n (-13+Sqrt[5])+(1+Sqrt[5])^n (13+Sqrt[5])))/Sqrt[5] - Herbert Kociemba (kociemba(AT)t-online.de)
|
|
|
MATHEMATICA
| a={}; b=1; c=7; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 9, 1}]; a (Vladimir Orlovsky, Jul 22 2008)
|
|
|
CROSSREFS
| a(n) = A101220(6, 0, n+1).
a(n) = A109754(6, n+1).
a(k) = A118654(3, k).
Cf. A131778.
Sequence in context: A165465 A047521 A070424 * A041100 A129658 A041693
Adjacent sequences: A022094 A022095 A022096 * A022098 A022099 A022100
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
| |
|
|
