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A022392
Fibonacci sequence beginning 1, 22.
1
1, 22, 23, 45, 68, 113, 181, 294, 475, 769, 1244, 2013, 3257, 5270, 8527, 13797, 22324, 36121, 58445, 94566, 153011, 247577, 400588, 648165, 1048753, 1696918, 2745671, 4442589, 7188260, 11630849, 18819109, 30449958, 49269067, 79719025, 128988092, 208707117, 337695209, 546402326
OFFSET
0,2
COMMENTS
a(n-1) = Sum_{k=0..ceiling((n-1)/2)} P(22;n-1-k,k), n>=1, with a(-1)=21. These are the SW-NE diagonals in P(22;n,k), the (22,1) 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.
FORMULA
a(n) = a(n-1) + a(n-2), n>=2, a(0)=1, a(1)=22. a(-1):=21.
G.f.: (1+21*x)/(1-x-x^2).
MATHEMATICA
Table[Fibonacci[n + 2] + 20*Fibonacci[n], {n, 0, 50}] (* or *) LinearRecurrence[{1, 1}, {1, 22}, 50] (* G. C. Greubel, Mar 02 2018 *)
PROG
(PARI) for(n=0, 50, print1(fibonacci(n+2) + 20*fibonacci(n), ", ")) \\ G. C. Greubel, Mar 02 2018
(Magma) [Fibonacci(n+2) + 20*Fibonacci(n): n in [0..50]]; // G. C. Greubel, Mar 02 2018
CROSSREFS
Sequence in context: A106556 A106554 A118297 * A041976 A041978 A041980
KEYWORD
nonn
EXTENSIONS
Terms a(30) onward added by G. C. Greubel, Mar 02 2018
STATUS
approved