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A022104 Fibonacci sequence beginning 1, 14. 3
1, 14, 15, 29, 44, 73, 117, 190, 307, 497, 804, 1301, 2105, 3406, 5511, 8917, 14428, 23345, 37773, 61118, 98891, 160009, 258900, 418909, 677809, 1096718, 1774527, 2871245, 4645772, 7517017, 12162789 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(n-1)=sum(P(14;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=13. These are the SW-NE diagonals in P(14;n,k), the (14,1) Pascal triangle. Cf. A093645 for the (10,1) Pascal triangle. Observation by Paul Barry, 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)=14. a(-1):=13.
G.f.: (1+13*x)/(1-x-x^2).
MATHEMATICA
a={}; b=1; c=14; 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 Joseph Stephan Orlovsky, Jul 22 2008 *)
LinearRecurrence[{1, 1}, {1, 14}, 40] (* Harvey P. Dale, Jun 12 2017 *)
PROG
(Magma) a0:=1; a1:=14; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..30]]; // Bruno Berselli, Feb 12 2013
CROSSREFS
a(n) = A109754(13, n+1) = A101220(13, 0, n+1).
Sequence in context: A087430 A085900 A075659 * A041398 A041919 A041400
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 29 01:36 EDT 2024. Contains 371264 sequences. (Running on oeis4.)