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 A022109 Fibonacci sequence beginning 1, 19. 3
 1, 19, 20, 39, 59, 98, 157, 255, 412, 667, 1079, 1746, 2825, 4571, 7396, 11967, 19363, 31330, 50693, 82023, 132716, 214739, 347455, 562194, 909649, 1471843, 2381492, 3853335, 6234827, 10088162, 16322989, 26411151, 42734140, 69145291, 111879431, 181024722 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n-1) = Sum(P(19;n-1-k,k),k=0..ceiling((n-1)/2)), n>=1, with a(-1)=18. These are the SW-NE diagonals in P(19;n,k), the (19,1) 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 Paolo Xausa, Table of n, a(n) for n = 0..1000 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (1,1). FORMULA a(n) = a(n-1)+a(n-2), n >= 2, a(0) = 1, a(1) = 19. G.f.: (1+18*x)/(1-x-x^2). MATHEMATICA LinearRecurrence[{1, 1}, {1, 19}, 35] (* Paolo Xausa, Feb 22 2024 *) PROG (Magma) a0:=1; a1:=19; [GeneralizedFibonacciNumber(a0, a1, n): n in [0..30]]; // Bruno Berselli, Feb 12 2013 CROSSREFS a(n) = A109754(18, n+1) = A101220(18, 0, n+1). Sequence in context: A241849 A054304 A151979 * A041730 A041732 A041728 Adjacent sequences: A022106 A022107 A022108 * A022110 A022111 A022112 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified August 10 05:56 EDT 2024. Contains 375044 sequences. (Running on oeis4.)