The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A022393 Fibonacci sequence beginning 1, 23. 1
 1, 23, 24, 47, 71, 118, 189, 307, 496, 803, 1299, 2102, 3401, 5503, 8904, 14407, 23311, 37718, 61029, 98747, 159776, 258523, 418299, 676822, 1095121, 1771943, 2867064, 4639007, 7506071, 12145078, 19651149, 31796227, 51447376, 83243603, 134690979, 217934582, 352625561, 570560143 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS a(n-1) = Sum_{k=0..ceiling((n-1)/2)} P(23;n-1-k,k), n>=1, with a(-1)=22. These are the SW-NE diagonals in P(23;n,k), the (23,1) 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 G. C. Greubel, 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)=23. a(-1):=22. G.f.: (1+22*x)/(1-x-x^2). MATHEMATICA a[1]=1; a[2]=23; a[n_]:=a[n]=a[n - 1]+a[n - 2] (* José María Grau Ribas, Feb 15 2010 *) LinearRecurrence[{1, 1}, {1, 23}, 30] (* Harvey P. Dale, Sep 30 2011 *) Table[Fibonacci[n + 2] + 21*Fibonacci[n], {n, 0, 50}] (* G. C. Greubel, Mar 02 2018 *) PROG (PARI) for(n=0, 50, print1(fibonacci(n+2) + 21*fibonacci(n), ", ")) \\ G. C. Greubel, Mar 02 2018 (Magma) [Fibonacci(n+2) + 21*Fibonacci(n): n in [0..50]]; // G. C. Greubel, Mar 02 2018 (GAP) List([0..40], n->Fibonacci(n+2)+21*Fibonacci(n)); # Muniru A Asiru, Mar 03 2018 CROSSREFS Sequence in context: A007638 A031332 A122470 * A042068 A042066 A042070 Adjacent sequences: A022390 A022391 A022392 * A022394 A022395 A022396 KEYWORD nonn AUTHOR N. J. A. Sloane EXTENSIONS Terms a(30) onward added by G. C. Greubel, Mar 02 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 14 21:14 EDT 2024. Contains 373401 sequences. (Running on oeis4.)