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 A022391 Fibonacci sequence beginning 1 21. 0
 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; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS 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, 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)=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 Joseph Stephan Orlovsky, Sep 18 2008] CROSSREFS Sequence in context: A141439 A125737 A160782 * A041890 A041892 A041894 Adjacent sequences:  A022388 A022389 A022390 * A022392 A022393 A022394 KEYWORD nonn AUTHOR STATUS approved

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