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A022110 Fibonacci sequence beginning 1, 20. 4
1, 20, 21, 41, 62, 103, 165, 268, 433, 701, 1134, 1835, 2969, 4804, 7773, 12577, 20350, 32927, 53277, 86204, 139481, 225685, 365166, 590851, 956017, 1546868, 2502885, 4049753, 6552638, 10602391, 17155029, 27757420, 44912449, 72669869, 117582318, 190252187 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
a(n-1) = Sum(P(20;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1) = 19. These are the SW-NE diagonals in P(20;n,k), the (20,1) 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) = 20.
G.f.: (1+19*x)/(1-x-x^2).
MATHEMATICA
a={}; b=1; c=20; AppendTo[a, b]; AppendTo[a, c]; Do[b=b+c; AppendTo[a, b]; c=b+c; AppendTo[a, c], {n, 1, 12, 1}]; a (* Vladimir Joseph Stephan Orlovsky, Jul 23 2008 *)
LinearRecurrence[{1, 1}, {1, 20}, 35] (* Paolo Xausa, Feb 22 2024 *)
PROG
(Magma) a0:=1; a1:=20; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..30]]; // Bruno Berselli, Feb 12 2013
CROSSREFS
a(n) = A109754(19, n+1) = A101220(19, 0, n+1).
Sequence in context: A176241 A075034 A363770 * A041808 A041810 A042855
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 19 04:26 EDT 2024. Contains 370952 sequences. (Running on oeis4.)