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A193656 Q-residue of the triangle p(n,k)=(2^(n - k))*5^k, 0<=k<=n, where Q is the triangular array (t(i,j)) given by t(i,j)=1. (See Comments.)

%I A193656 #9 Feb 19 2015 14:49:15
%S A193656 1,7,43,247,1363,7327,38683,201607,1040803,5335087,27199723,138095767,
%T A193656 698867443,3527891647,17773675963,89405250727,449173737283,
%U A193656 2254458621007,11306652843403,56670703170487,283903271666323
%N A193656 Q-residue of the triangle p(n,k)=(2^(n - k))*5^k, 0<=k<=n, where Q is the triangular array (t(i,j)) given by t(i,j)=1.  (See Comments.)
%C A193656 For the definition of Q-residue, see A193649.
%F A193656 Conjecture: a(n) = 3*5^n-2*4^n; G.f.: ( 1-2*x ) / ( (5*x-1)*(4*x-1) ). - _R. J. Mathar_, Feb 19 2015
%t A193656 q[n_, k_] := 1;
%t A193656 r[0] = 1; r[k_] := Sum[q[k - 1, i] r[k - 1 - i], {i, 0, k - 1}]
%t A193656 p[n_, k_] := (2^(n - k))*5^k
%t A193656 v[n_] := Sum[p[n, k] r[n - k], {k, 0, n}]
%t A193656 Table[v[n], {n, 0, 20}]    (* A193656 *)
%t A193656 TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]
%t A193656 Table[r[k], {k, 0, 8}]  (*  *)
%t A193656 TableForm[Table[p[n, k], {n, 0, 4}, {k, 0, n}]]
%Y A193656 Cf. A193649.
%K A193656 nonn
%O A193656 0,2
%A A193656 _Clark Kimberling_, Aug 02 2011