login
A022391
Fibonacci sequence beginning 1, 21.
2
1, 21, 22, 43, 65, 108, 173, 281, 454, 735, 1189, 1924, 3113, 5037, 8150, 13187, 21337, 34524, 55861, 90385, 146246, 236631, 382877, 619508, 1002385, 1621893, 2624278, 4246171, 6870449, 11116620, 17987069, 29103689, 47090758, 76194447, 123285205, 199479652, 322764857, 522244509
OFFSET
0,2
COMMENTS
a(n-1) = Sum_{k=0..ceiling((n-1)/2)} P(21;n-1-k,k), n>=1, with a(-1)=20. These are the SW-NE diagonals in P(21;n,k), the (21,1) 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
S. Kak, The Golden Mean and the Physics of Aesthetics, arXiv:physics/0411195 [physics.hist-ph], 2004.
Tanya Khovanova, Recursive Sequences
FORMULA
a(n) = a(n-1) + a(n-2), n>=2, a(0)=1, a(1)=21. a(-1):=20.
G.f.: (1+20*x)/(1-x-x^2).
MATHEMATICA
LinearRecurrence[{1, 1}, {1, 21}, 30] (* Jean-François Alcover, Feb 25 2018 *)
Table[Fibonacci[n + 2] + 19*Fibonacci[n], {n, 0, 50}] (* G. C. Greubel, Mar 02 2018 *)
PROG
(PARI) for(n=0, 50, print1(fibonacci(n+2) + 19*fibonacci(n), ", ")) \\ G. C. Greubel, Mar 02 2018
(Magma) [Fibonacci(n+2) + 19*Fibonacci(n): n in [0..50]]; // G. C. Greubel, Mar 02 2018
CROSSREFS
Sequence in context: A125737 A349248 A160782 * A041890 A041892 A041894
KEYWORD
nonn
EXTENSIONS
Terms a(30) onward added by G. C. Greubel, Mar 02 2018
STATUS
approved