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.)

1, 7, 43, 247, 1363, 7327, 38683, 201607, 1040803, 5335087, 27199723, 138095767, 698867443, 3527891647, 17773675963, 89405250727, 449173737283, 2254458621007, 11306652843403, 56670703170487, 283903271666323

Offset: 0

Author

Clark Kimberling, Aug 02 2011

Keywords

• nonn

Comments

For the definition of Q-residue, see A193649.

Crossrefs

Cf. A193649.

Programs

Mathematica

q[n_, k_] := 1;
r[0] = 1; r[k_] := Sum[q[k - 1, i] r[k - 1 - i], {i, 0, k - 1}]
p[n_, k_] := (2^(n - k))*5^k
v[n_] := Sum[p[n, k] r[n - k], {k, 0, n}]
Table[v[n], {n, 0, 20}]    (* A193656 *)
TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]
Table[r[k], {k, 0, 8}]  (*  *)
TableForm[Table[p[n, k], {n, 0, 4}, {k, 0, n}]]

Formula

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