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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

N. J. A. Sloane

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.)