A137500 Binomial transform of b(n) = (0, 0, A007910).

0, 0, 1, 5, 17, 51, 149, 439, 1309, 3927, 11797, 35423, 106301, 318903, 956645, 2869807, 8609293, 25827879, 77483893, 232452191, 697357085, 2092071255, 6276212741, 18828636175, 56485906477, 169457719431, 508373162389, 1525119495359, 4575358494269, 13726075482807

Offset: 0

Author

Paul Curtz, Apr 27 2008

Keywords

• nonn
• easy

Comments

b(n) is binomial transform of (0, 0, A077973).

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-8,6).

Crossrefs

Cf. A007910, A009545.

Programs

Mathematica

LinearRecurrence[{5,-8,6},{0,0,1},40] (* Harvey P. Dale, Sep 27 2020 *)

PARI

concat([0,0], Vec(1/((1 - 3*x)*(1 - 2*x + 2*x^2)) + O(x^40))) \\ Andrew Howroyd, Jan 03 2020

Formula

a(n) = 3*a(n-1) + A009545(n-1) for n > 0.

From Andrew Howroyd, Jan 03 2020: (Start)

a(n) = Sum_{k=0..n-2} binomial(n, k+2)*A007910(k).

a(n) = 5*a(n-1) - 8*a(n-2) + 6*a(n-3) for n >= 3.

G.f.: x*2/((1 - 3*x)*(1 - 2*x + 2*x^2)). (End)

Extensions

Terms a(11) and beyond from Andrew Howroyd, Jan 03 2020