This site is supported by donations to The OEIS Foundation.

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A123185 Triangular array from a zero coefficient sum of recursive polynomials: p(k, x) = x*p(k - 1, x) + p(k - 2, x). 1
 1, -1, 1, 2, -3, 1, -1, 3, -3, 1, 2, -4, 4, -3, 1, -1, 5, -7, 5, -3, 1, 2, -5, 9, -10, 6, -3, 1, -1, 7, -12, 14, -13, 7, -3, 1, 2, -6, 16, -22, 20, -16, 8, -3, 1, -1, 9, -18, 30, -35, 27, -19, 9, -3, 1, 2, -7, 25, -40, 50, -51, 35, -22, 10, -3, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 COMMENTS Except for p(0,x)=1 all sum to zero: Table[Sum[CoefficientList[p[n, x], x][[m]], {m, 1, n + 1}], {n, 0, 12}] {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0} LINKS Robert Israel, Table of n, a(n) for n = 0..10010 (rows 0 to 140, flattened) FORMULA p(k, x) = x*p(k - 1, x) + p(k - 2, x)  for k >= 3 with p(0,x) = 1, p(1,x) = x-1 and p(2,x) = x^2-3x+2. (Corrected by Robert Israel, Jul 12 2016) G.f.: g(t,x) = (1 - t + (1-2x) t^2)/(1 - t x - t^2). - Robert Israel, Jul 12 2016 For n >= 1, T(n,k) = A114525(n,k) + 2*A114525(n-1,k) - 5*A168561(n-1,k), where we take A114525(n-1,n) = A168561(n-1,n) = 0. - Robert Israel, Jul 13 2016 EXAMPLE 1 -1, 1 2, -3, 1 -1, 3, -3, 1 2, -4, 4, -3, 1 -1, 5, -7, 5, -3, 1 2, -5, 9, -10, 6, -3, 1 MAPLE S:= series((1 - t + (1-2*x)*t^2)/(1 - t*x - t^2), t, 21): R:= [seq(coeff(S, t, n), n=0..19)]: seq(seq(coeff(R[n], x, j), j=0..n-1), n=1..20); # Robert Israel, Jul 12 2016 MATHEMATICA p[0, x] = 1; p[1, x] = x - 1; p[2, x] = x^2 - 3x + 2; p[k_, x_] := p[k, x] = x*p[k - 1, x] + p[k - 2, x] ; w = Table[CoefficientList[p[n, x], x], {n, 0, 10}]; Flatten[w] CROSSREFS Cf. A114525, A168561. Sequence in context: A077233 A282290 A178795 * A133569 A141071 A004648 Adjacent sequences:  A123182 A123183 A123184 * A123186 A123187 A123188 KEYWORD tabl,sign AUTHOR Roger L. Bagula, Oct 02 2006 EXTENSIONS Edited by Robert Israel, Jul 13 2016 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 January 16 12:10 EST 2019. Contains 319192 sequences. (Running on oeis4.)