A221863 Expansion of (1-3*x+x^2)/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).

1, 6, 27, 110, 429, 1637, 6172, 23104, 86090, 319792, 1185305, 4386331, 16212913, 59873834, 220964744, 815057639, 3005282745, 11077802256, 40824723483, 150424044413, 554183037617, 2041477665799, 7519722443381, 27696997721940, 102010147865915, 375697698147882

Offset: 0

Author

Philippe Deléham, Apr 10 2013

Keywords

• nonn
• easy

Comments

A diagonal of the square array A223968.

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..1765
• László Németh and László Szalay, Sequences Involving Square Zig-Zag Shapes, J. Int. Seq., Vol. 24 (2021), Article 21.5.2.
• Index entries for linear recurrences with constant coefficients, signature (9,-28,35,-15,1).

Crossrefs

Cf. A223968

Programs

Mathematica

CoefficientList[Series[(1-3x+x^2)/(1-9x+28x^2-35x^3+15x^4-x^5),{x,0,30}],x] (* or *) LinearRecurrence[{9,-28,35,-15,1},{1,6,27,110,429},30] (* Harvey P. Dale, Jan 26 2015 *)

Formula

a(n) = A223968(n,n+4) = A223968(n,n+5).

G.f.: (1-3*x+x^2)/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).

a(n) = 9*a(n-1) - 28*a(n-2) + 35*a(n-3) - 15*a(n-4) + a(n-5) with a(0) = 1, a(1) = 6, a(2) = 27, a(3) = 110, a(4) = 429.