OFFSET
0,4
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..60
FORMULA
a(n) = a(n-1) + 9^(n-2) * a(n-2).
MAPLE
q:=9; 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 16 2019
MATHEMATICA
RecurrenceTable[{a[0]==0, a[1]==1, a[n]==a[n-1] + a[n-2]*9^(n-2)}, a, {n, 20}] (* 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, 9], {n, 0, 20}] (* G. C. Greubel, Dec 16 2019 *)
PROG
(Magma) [0] cat[n le 2 select 1 else Self(n-1) + Self(n-2)*(9^(n-2)): n in [1..15]]; // Vincenzo Librandi, Nov 09 2012
(PARI) q=9; 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 16 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, 9) for n in (0..20)] # G. C. Greubel, Dec 16 2019
(GAP) q:=9;; 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 16 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved