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 A204922 Ordered differences of Fibonacci numbers. 32
 1, 2, 1, 4, 3, 2, 7, 6, 5, 3, 12, 11, 10, 8, 5, 20, 19, 18, 16, 13, 8, 33, 32, 31, 29, 26, 21, 13, 54, 53, 52, 50, 47, 42, 34, 21, 88, 87, 86, 84, 81, 76, 68, 55, 34, 143, 142, 141, 139, 136, 131, 123, 110, 89, 55, 232, 231, 230, 228, 225, 220, 212, 199, 178 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS For a guide to related sequences, see A204892. For numbers not in A204922, see A050939. From Emanuele Munarini, Mar 29 2012: (Start) Triangle begins:    1;    2,  1;    4,  3,  2;    7,  6,  5,  3;   12, 11, 10,  8,  5;   20, 19, 18, 16, 13,  8;   33, 32, 31, 29, 26, 21, 13;   54, 53, 52, 50, 47, 42, 34, 21;   88, 87, 86, 84, 81, 76, 68, 55, 34; Diagonal elements = Fibonacci numbers F(n+1) (A000045) First column = Fibonacci numbers - 1 (A000071); Second column = Fibonacci numbers - 2 (A001911); Row sums = n*F(n+3) - F(n+2) + 2 (A014286); Central coefficients = F(2*n+1) - F(n+1) (A096140). (End) LINKS G. C. Greubel, Rows n=1..100 of triangle, flattened FORMULA From Emanuele Munarini, Mar 29 2012: (Start) T(n,k) = Fibonacci(n+2) - Fibonacci(k+1). T(n,k) = Sum_{i=k..n} Fibonacci(i+1). (End) EXAMPLE a(1) = s(2) - s(1) = F(3) - F(2) = 2-1 = 1, where F=A000045; a(2) = s(3) - s(1) = F(4) - F(2) = 3-1 = 2; a(3) = s(3) - s(2) = F(4) - F(3) = 3-2 = 1; a(4) = s(4) - s(1) = F(5) - F(2) = 5-1 = 4. MATHEMATICA (See the program at A204924.) PROG (Maxima) create_list(fib(n+3)-fib(k+2), n, 0, 20, k, 0, n); /* Emanuele Munarini */ (MAGMA) /* As triangle */ [[Fibonacci(n+2)-Fibonacci(k+1) : k in [1..n]]: n in [1.. 15]]; // Vincenzo Librandi, Aug 04 2015 (PARI) {T(n, k) = fibonacci(n+2) - fibonacci(k+1)}; for(n=1, 15, for(k=1, n, print1(T(n, k), ", "))) \\ G. C. Greubel, Feb 03 2019 (Sage) [[fibonacci(n+2) - fibonacci(k+1) for k in (1..n)] for n in (1..15)] # G. C. Greubel, Feb 03 2019 CROSSREFS Cf. A204924, A204892. Sequence in context: A287010 A144330 A141155 * A057669 A243610 A182013 Adjacent sequences:  A204919 A204920 A204921 * A204923 A204924 A204925 KEYWORD nonn AUTHOR Clark Kimberling, Jan 21 2012 STATUS approved

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Last modified June 30 02:41 EDT 2022. Contains 354913 sequences. (Running on oeis4.)