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A015485 q-Fibonacci numbers for q=12. 12
0, 1, 12, 1729, 2987724, 61953446593, 15416000025617100, 46031929420554204172993, 1649407256866864913519509578444, 709214929702322267749941478181800334017, 3659393259623103647557638545139154960967463412428 (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) = 12^(n-1)*a(n-1) + a(n-2).

MAPLE

q:=12; 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 19 2019

MATHEMATICA

RecurrenceTable[{a[0]==0, a[1]==1, a[n]==a[n-1]*12^(n-1)+ a[n-2]}, a, {n, 20}] (* Vincenzo Librandi, Nov 10 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, 12], {n, 0, 20}] (* G. C. Greubel, Dec 19 2019 *)

PROG

(PARI) q=12; 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 19 2019

(MAGMA) q:=12; 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 19 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, 12) for n in (0..20)] # G. C. Greubel, Dec 19 2019

(GAP) q:=12;; 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 19 2019

CROSSREFS

q-Fibonacci numbers: A280222 (q=-3), A280221 (q=-2), A280261 (q=-1), A000045 (q=1), A015473 (q=2), A015474 (q=3), A015475 (q=4), A015476 (q=5), A015477 (q=6), A015479 (q=7), A015480 (q=8), A015481 (q=9), A015482 (q=10), A015484 (q=11), this sequence (q=12).

Differs from A015470.

Sequence in context: A202968 A013717 A252767 * A174775 A145186 A160304

Adjacent sequences:  A015482 A015483 A015484 * A015486 A015487 A015488

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified May 17 04:46 EDT 2022. Contains 353730 sequences. (Running on oeis4.)