A110667 - OEIS

%I #16 Sep 04 2017 23:29:29

%S 0,1,2,0,-6,-12,-12,-5,2,0,-12,-24,-24,-11,2,0,-18,-36,-36,-17,2,0,

%T -24,-48,-48,-23,2,0,-30,-60,-60,-29,2,0,-36,-72,-72,-35,2,0,-42,-84,

%U -84,-41,2,0,-48,-96,-96,-47,2,0,-54,-108,-108,-53,2,0,-60,-120,-120,-59,2,0,-66,-132,-132,-65,2,0,-72,-144,-144,-71,2,0

%N Sequence is {a(2,n)}, where a(m,n) is defined at sequence A110665.

%H Michael De Vlieger, <a href="/A110667/b110667.txt">Table of n, a(n) for n = 0..1000</a>

%F Conjecture: g.f.: -x*(-1+2*x) / ( (x-1)^2*(x^2-x+1)^2 ). - _R. J. Mathar_, Oct 09 2013

%e a(0,n): 0,  1,  0, -3, -4, ...

%e a(1,n): 0,  1,  1, -2, -6, ...

%e a(2,n): 0,  1,  2,  0, -6, ...

%e a(3,n): 0,  1,  3,  3, -3, ...

%e a(4,n): 0,  1,  4,  7,  4, ...

%e Main diagonal of array is 0, 1, 2, 3, 4, ...

%p A11066x := proc(mmax,nmax) local a,i,j ; a := array(0..mmax,0..nmax) ; a[0,0] := 0 ; for i from 1 to nmax do a[0,i] := i-sum(binomial(2*i-k-1,i-1)*a[0,k],k=0..i-1) : od ; for j from 1 to mmax do a[j,0] := 0 ; for i from 1 to nmax do a[j,i] := a[j-1,i]+a[j,i-1] ; od ; od ; RETURN(a) ; end :

%p nmax := 100 : m := 2: a := A11066x(m,nmax) :

%p for n from 0 to nmax do printf("%d,",a[m,n]) ; od ; # _R. J. Mathar_, Sep 01 2006

%t a[m_, n_] := a[m, n] = Which[n == 0, 0, m == 0, n - Sum[ Binomial[2 n - k - 1, n - 1]*a[0, k], {k, 0, (n - 1)}], True, a[m - 1, n] + a[m, n - 1]]; Array[a[2, #] &, 76, 0] (* _Michael De Vlieger_, Sep 04 2017 *)

%Y Cf. A110665 - A110672.

%K easy,sign

%O 0,3

%A _Leroy Quet_, Aug 02 2005

%E More terms from _R. J. Mathar_, Sep 01 2006