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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 (list; graph; refs; listen; history; text; internal format)
 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. 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)=22. a(-1):=21. G.f.: (1+21*x)/(1-x-x^2). a(n) = 22*A000045(n) + A000045(n-1). - Paolo P. Lava, May 19 2015 MAPLE with(numtheory): with(combinat): P:=proc(q) local n; for n from 0 to q do print(22*fibonacci(n)+fibonacci(n-1)); od; end: P(30); # Paolo P. Lava, May 19 2015 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 Adjacent sequences:  A022389 A022390 A022391 * A022393 A022394 A022395 KEYWORD nonn AUTHOR EXTENSIONS Terms a(30) onward added by G. C. Greubel, Mar 02 2018 STATUS approved

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Last modified December 10 19:01 EST 2018. Contains 318049 sequences. (Running on oeis4.)