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A022392 Fibonacci sequence beginning 1 22. 0
1, 22, 23, 45, 68, 113, 181, 294, 475, 769, 1244, 2013, 3257, 5270, 8527, 13797, 22324, 36121, 58445, 94566, 153011, 247577, 400588, 648165, 1048753, 1696918, 2745671, 4442589, 7188260, 11630849 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n-1)=sum(P(22;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=21. These are the SW-NE diagonals in P(22;n,k), the (22,1) 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

Table of n, a(n) for n=0..29.

Tanya Khovanova, Recursive Sequences

FORMULA

a(n)= a(n-1)+a(n-2), n>=2, a(0)=1, a(1)=22. a(-1):=21.

G.f.: (1+21*x)/(1-x-x^2).

MATHEMATICA

a={}; b=1; c=22; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 4!}]; a [From Vladimir Joseph Stephan Orlovsky, Sep 18 2008]

CROSSREFS

Sequence in context: A106556 A106554 A118297 * A041976 A041978 A041980

Adjacent sequences:  A022389 A022390 A022391 * A022393 A022394 A022395

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified April 16 18:58 EDT 2014. Contains 240627 sequences.