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 A015470 q-Fibonacci numbers for q=12. 12
 0, 1, 1, 13, 157, 22621, 3278173, 5632106845, 9794204234077, 201818365309759837, 4211530365904119214429, 1041342647528423104910537053, 260767900948768868884822059725149, 773726564635922870118341112574642827613 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..60 FORMULA a(n) = a(n-1) + 12^(n-2)*a(n-2). MAPLE q:=12; seq(add((product((1-q^(n-j-1-k))/(1-q^(k+1)), k=0..j-1))*q^(j^2), j = 0..floor((n-1)/2)), n = 0..20); # G. C. Greubel, Dec 17 2019 MATHEMATICA RecurrenceTable[{a[0]==0, a[1]==1, a[n]==a[n-1]+a[n-2]*12^(n-2)},  a, {n, 60}] (* Vincenzo Librandi, Nov 09 2012 *) F[n_, q_]:= Sum[QBinomial[n-j-1, j, q]*q^(j^2), {j, 0, Floor[(n-1)/2]}]; Table[F[n, 12], {n, 0, 20}] (* G. C. Greubel, Dec 17 2019 *) PROG (MAGMA) [0] cat[n le 2 select 1 else Self(n-1) + Self(n-2)*(12^(n-2)): n in [1..15]]; // Vincenzo Librandi, Nov 09 2012 (PARI) q=12; m=20; v=concat([0, 1], vector(m-2)); for(n=3, m, v[n]=v[n-1]+q^(n-3)*v[n-2]); v \\ G. C. Greubel, Dec 17 2019 (Sage) def F(n, q): return sum( q_binomial(n-j-1, j, q)*q^(j^2) for j in (0..floor((n-1)/2))) [F(n, 12) for n in (0..20)] # G. C. Greubel, Dec 17 2019 (GAP) q:=12;; a:=[0, 1];; for n in [3..20] do a[n]:=a[n-1]+q^(n-3)*a[n-2]; od; a; # G. C. Greubel, Dec 17 2019 CROSSREFS q-Fibonacci numbers: A000045 (q=1), A015459 (q=2), A015460 (q=3), A015461 (q=4), A015462 (q=5), A015463 (q=6), A015464 (q=7), A015465 (q=8), A015467 (q=9), A015468 (q=10), A015469 (q=11), this sequence (q=12). Sequence in context: A165151 A016125 A175519 * A084328 A000830 A205170 Adjacent sequences:  A015467 A015468 A015469 * A015471 A015472 A015473 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified February 24 09:21 EST 2020. Contains 332209 sequences. (Running on oeis4.)