A224422 Expansion of (1-x)*(1-3*x)/(1-9*x+28*x^2-35*x^3+15*x^4-x^5).

1, 5, 20, 75, 275, 1001, 3639, 13243, 48280, 176341, 645150, 2363596, 8669142, 31825005, 116914020, 429737220, 1580244061, 5812839156, 21387636101, 78708626396, 289699273501, 1066406842677, 3925882147566, 14453780545834, 53216783798234, 195944670698910

Offset: 0

Author

Philippe Deléham, Apr 06 2013

Keywords

• nonn
• easy

Comments

A diagonal of the square array A223968.

Links

• Michael De Vlieger, Table of n, a(n) for n = 0..1766
• 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

LinearRecurrence[{9, -28, 35, -15, 1}, {1, 5, 20, 75, 275}, 26] (* Michael De Vlieger, Aug 05 2021 *)

Formula

a(n) = A223968(n+3,n) = A223968(n+4,n).

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) = 5, a(2) = 20, a(3) = 75, a(4) = 275.