A193661 Q-residue of the triangle A193673, where Q is the triangular array (t(i,j)) given by t(i,j)=1. (See Comments.)

1, 3, 15, 93, 621, 4263, 29595, 206433, 1442841, 10093323, 70633575, 494375973, 3460454661, 24222651183, 169556963955, 1186893964713, 8308243404081, 58157660781843, 407103496332735, 2849724086908653, 19948067446099101

Offset

0,2

Comments

See A193649 for the definition of Q-residue.

Links

Table of n, a(n) for n=0..20.

Formula

Conjecture: G.f.: ( -1+8*x-13*x^2 ) / ( (x-1)*(3*x-1)*(7*x-1) ). - R. J. Mathar, Feb 19 2015

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_] := Coefficient[(1/2) ((x + 3)^n + (x + 1)^n), x, k] (* A193673 *)
v[n_] := Sum[p[n, k] r[n - k], {k, 0, n}]
Table[v[n], {n, 0, 20}]    (* A193661 *)
TableForm[Table[q[i, k], {i, 0, 4}, {k, 0, i}]]
Table[r[k], {k, 0, 8}]  (* 2^k *)
TableForm[Table[p[n, k], {n, 0, 10}, {k, 0, n}]] (* A193673 as a triangle *)
Flatten[%] (* A193673 as a sequence *)

Crossrefs

Cf. A193649, A193673.

Sequence in context: A231657 A361881 A303558 * A192296 A370218 A002893

Adjacent sequences: A193658 A193659 A193660 * A193662 A193663 A193664

Keyword

nonn

Author

Clark Kimberling, Aug 02 2011

Status

approved