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A193662 Q-residue of the Lucas triangle A114525, where Q is the triangle given by t(i,j)=1 for 0<=i<=j.  (See Comments.) 2

%I

%S 2,1,5,7,25,51,149,351,945,2347,6125,15511,40009,102051,262085,670287,

%T 1718625,4399771,11274269,28873351

%N Q-residue of the Lucas triangle A114525, where Q is the triangle given by t(i,j)=1 for 0<=i<=j. (See Comments.)

%C For the definition of Q-residue, see A193649.

%F Conjecture: a(n) = 2*a(n-1) +3*a(n-2) -4*a(n-3) if n>3. - _R. J. Mathar_, Feb 19 2015

%t q[n_, k_] := 1;

%t r[0] = 1; r[k_] := Sum[q[k - 1, i] r[k - 1 - i], {i, 0, k - 1}];

%t f[n_, x_] := LucasL[n, x]; (* A114525 *)

%t p[n_, k_] := Coefficient[f[n, x], x, k];

%t v[n_] := Sum[p[n, k] r[n - k], {k, 0, n}]

%t Table[v[n], {n, 0, 16}] (* A193662 *)

%t TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]

%t Table[r[k], {k, 0, 8}]

%t TableForm[Table[p[n, k], {n, 0, 4}, {k, 0, 4}]]

%Y Cf. A193649, A114525.

%K nonn

%O 0,1

%A _Clark Kimberling_, Aug 02 2011

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Last modified September 25 06:32 EDT 2020. Contains 337335 sequences. (Running on oeis4.)