This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A159764 Riordan array (1/(1+4x+x^2), x/(1+4x+x^2)). 13

%I

%S 1,-4,1,15,-8,1,-56,46,-12,1,209,-232,93,-16,1,-780,1091,-592,156,-20,

%T 1,2911,-4912,3366,-1200,235,-24,1,-10864,21468,-17784,8010,-2120,330,

%U -28,1,40545,-91824,89238,-48624,16255,-3416,441,-32,1,-151316,386373

%N Riordan array (1/(1+4x+x^2), x/(1+4x+x^2)).

%C Row sums are (-1)^n*F(2n+2). Diagonal sums are (-1)^n*4^n. Inverse is A052179.

%C The positive matrix is (1/(1-4x+x^2), x/(1-4x+x^2)) with general term T(n,k) = if(k<=n, Gegenbauer_C(n-k,k+1,2),0).

%C For another version, see A124029.

%C Triangle of coefficients of Chebyshev's S(n,x-4) polynomials (exponents of x in increasing order). - _Philippe Deléham_, Feb 22 2012

%C Subtriangle of triangle given by (0, -4, 1/4, -1/4, 0, 0, 0, 0, 0, 0, 0, ...) DELTA (1, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - _Philippe Deléham_, Feb 22 2012

%H G. C. Greubel, <a href="/A159764/b159764.txt">Rows n=0..100 of triangle, flattened</a>

%F Number triangle T(n,k) = if(k<=n, Gegenbauer_C(n-k,k+1,-2),0).

%F G.f.: 1/(1+4*x+x^2-y*x). - _Philippe Deléham_, Feb 22 2012

%F T(n,k) = (-4)*T(n-1,k) + T(n-1,k-1) - T(n-2,k). - _Philippe Deléham_, Feb 22 2012

%e Triangle begins

%e 1;

%e -4, 1;

%e 15, -8, 1;

%e -56, 46, -12, 1;

%e 209, -232, 93, -16, 1;

%e -780, 1091, -592, 156, -20, 1;

%e 2911, -4912, 3366, -1200, 235, -24, 1;

%e Triangle (0, -4, 1/4, -1/4, 0, 0, 0, ...) DELTA (1, 0, 0, 0, ...) begins:

%e 1;

%e 0, 1;

%e 0, -4, 1;

%e 0, 15, -8, 1;

%e 0, -56, 46, -12, 1;

%e 0, 209, -232, 93, -16, 1;

%t CoefficientList[CoefficientList[Series[1/(1 + 4*x + x^2 - y*x), {x, 0, 10}, {y, 0, 10}], x], y]//Flatten (* _G. C. Greubel_, May 21 2018 *)

%o (Sage)

%o @CachedFunction

%o def A159764(n,k):

%o if n< 0: return 0

%o if n==0: return 1 if k == 0 else 0

%o return A159764(n-1,k-1)-A159764(n-2,k)-4*A159764(n-1,k)

%o for n in (0..9): [A159764(n,k) for k in (0..n)] # _Peter Luschny_, Nov 20 2012

%Y Cf. Triangle of coefficients of Chebyshev's S(n,x+k) polynomials : A207824, A207823, A125662, A078812, A101950, A049310, A104562, A053122, A207815, A159764, A123967 for k = 5, 4, 3, 2, 1, 0, -1, -2, -3, -4, -5 respectively.

%K easy,sign,tabl

%O 0,2

%A _Paul Barry_, Apr 21 2009

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 December 15 11:43 EST 2019. Contains 329999 sequences. (Running on oeis4.)