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A015481 q-Fibonacci numbers for q=9. 14
0, 1, 9, 730, 532179, 3491627149, 206177092053480, 109570959981485091829, 524074504891889945272313781, 22559688995294431207802541840253930, 8740085742244887761578226267084082717085551 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..40

FORMULA

a(n) = 9^(n-1)*a(n-1) + a(n-2).

MAPLE

q:=9; seq(add((product((1-q^(2*(n-j-1-k)))/(1-q^(2*k+2)), k=0..j-1))* q^binomial(n-2*j, 2), j = 0..floor((n-1)/2)), n = 0..20); # G. C. Greubel, Dec 18 2019

MATHEMATICA

RecurrenceTable[{a[0]==0, a[1]==1, a[n]==9^(n-1) a[n-1]+a[n-2]}, a[n], {n, 10}] (* Harvey P. Dale, Aug 24 2012 *)

F[n_, q_]:= Sum[QBinomial[n-j-1, j, q^2]*q^Binomial[n-2*j, 2], {j, 0, Floor[(n-1)/2]}]; Table[F[n, 9], {n, 0, 20}] (* G. C. Greubel, Dec 18 2019 *)

PROG

(PARI) q=9; m=20; v=concat([0, 1], vector(m-2)); for(n=3, m, v[n]=q^(n-2)*v[n-1]+v[n-2]); v \\ G. C. Greubel, Dec 18 2019

(MAGMA) q:=9; I:=[0, 1]; [n le 2 select I[n] else q^(n-2)*Self(n-1) + Self(n-2): n in [1..20]]; // G. C. Greubel, Dec 18 2019

(Sage)

def F(n, q): return sum( q_binomial(n-j-1, j, q^2)*q^binomial(n-2*j, 2) for j in (0..floor((n-1)/2)))

[F(n, 9) for n in (0..20)] # G. C. Greubel, Dec 18 2019

(GAP) q:=9;; a:=[0, 1];; for n in [3..20] do a[n]:=q^(n-2)*a[n-1]+a[n-2]; od; a; # G. C. Greubel, Dec 18 2019

CROSSREFS

q-Fibonacci numbers: A000045 (q=1), A015473 (q=2), A015474 (q=3), A015475 (q=4), A015476 (q=5), A015477 (q=6), A015479 (q=7), A015480 (q=8), this sequence (q=9), A015482 (q=10), A015484 (q=11), A015485 (q=12).

Differs from A015467.

Sequence in context: A255510 A122251 A234611 * A229930 A185274 A246122

Adjacent sequences:  A015478 A015479 A015480 * A015482 A015483 A015484

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified August 17 22:43 EDT 2022. Contains 356195 sequences. (Running on oeis4.)