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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
Tanya Khovanova, Recursive Sequences
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
Terms a(30) onward added by G. C. Greubel, Mar 02 2018
STATUS
approved

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