The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A136688 Triangular sequence of q-Fibonacci polynomials for s=2: F(x,n) = x*F(x,n-1) + s*F(x,n-2). 2
 1, 0, 1, 2, 0, 1, 0, 4, 0, 1, 4, 0, 6, 0, 1, 0, 12, 0, 8, 0, 1, 8, 0, 24, 0, 10, 0, 1, 0, 32, 0, 40, 0, 12, 0, 1, 16, 0, 80, 0, 60, 0, 14, 0, 1, 0, 80, 0, 160, 0, 84, 0, 16, 0, 1, 32, 0, 240, 0, 280, 0, 112, 0, 18, 0, 1, 0, 192, 0, 560, 0, 448, 0, 144, 0, 20, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS Row sums are: 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, ... = A001045(n). Riordan array (1/(1-2*x^2), x/(1-2*x^2)). - Paul Barry, Jun 18 2008 Diagonal sums are 1,0,3,0,9,... with g.f. 1/(1-3*x^2). - Paul Barry, Jun 18 2008 LINKS G. C. Greubel, Rows n = 1..100 of triangle, flattened (terms 1..500 from Nathaniel Johnston) J. Cigler, q-Fibonacci polynomials, Fibonacci Quarterly 41 (2003) 31-40. FORMULA F(x,n) = x*F(x,n-1) + s*F(x,n-2), where F(x,0)=0, F(x,1)=1 and s=2. EXAMPLE Triangle begins as:    1;    0,  1;    2,  0,   1;    0,  4,   0,   1;    4,  0,   6,   0,   1;    0, 12,   0,   8,   0,  1;    8,  0,  24,   0,  10,  0,   1;    0, 32,   0,  40,   0, 12,   0,  1;   16,  0,  80,   0,  60,  0,  14,  0,  1;    0, 80,   0, 160,   0, 84,   0, 16,  0, 1;   32,  0, 240,   0, 280,  0, 112,  0, 18, 0, 1; ... MAPLE A136688 := proc(n) option remember: if(n<=1)then return n: else return x*A136688(n-1)+2*A136688(n-2): fi: end: seq(seq(coeff(A136688(n), x, m), m=0..n-1), n=1..10); # Nathaniel Johnston, Apr 27 2011 MATHEMATICA s = 2; F[x_, n_]:= F[x, n]= If[n<2, n, x*F[x, n-1] + s*F[x, n-2]]; Table[CoefficientList[F[x, n], x], {n, 12}]//Flatten F[n_, x_, s_, q_]:= Sum[QBinomial[n-j-1, j, q]*q^Binomial[j+1, 2]*x^(n-2*j-1) *s^j, {j, 0, Floor[(n-1)/2]}]; Table[CoefficientList[F[n, x, 2, 1], x], {n, 1, 10}]//Flatten (* G. C. Greubel, Dec 16 2019 *) PROG (Sage) def f(n, x, s, q): return sum( q_binomial(n-j-1, j, q)*q^binomial(j+1, 2)*x^(n-2*j-1)*s^j for j in (0..floor((n-1)/2))) def A136688_list(prec):     P. = PowerSeriesRing(ZZ, prec)     return P( f(n, x, 2, 1) ).list() [A136688_list(n) for n in (1..10)] # G. C. Greubel, Dec 16 2019 CROSSREFS Cf. A136689, A136705. Sequence in context: A073430 A053389 A202328 * A131321 A111959 A110109 Adjacent sequences:  A136685 A136686 A136687 * A136689 A136690 A136691 KEYWORD nonn,easy,tabl AUTHOR Roger L. Bagula, Apr 06 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 29 21:32 EDT 2020. Contains 333117 sequences. (Running on oeis4.)