A087449 a(n) = n * 4^(n-1) + (2*4^n + 1) / 3.

1, 4, 19, 91, 427, 1963, 8875, 39595, 174763, 764587, 3320491, 14330539, 61516459, 262843051, 1118481067, 4742359723, 20043180715, 84467690155, 355050629803, 1488921995947, 6230565890731, 26021775190699, 108485147273899

Offset: 0

Author

Paul Barry, Sep 05 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A064017.

Links

• Index entries for linear recurrences with constant coefficients, signature (9,-24,16).

Crossrefs

Cf. A002697, A007583, A064017.

Programs

Mathematica

LinearRecurrence[{9,-24,16},{1,4,19},30] (* Harvey P. Dale, Apr 15 2018 *)

PARI

a(n) = my(p4 = 1<<(2*n)); n * p4 / 4 + (2*p4 + 1) / 3 \\ David A. Corneth, Apr 15 2018

Formula

G.f.: (1-5x+7x^2)/((1-x)(1-4x)^2).

a(n) = A002697(n) + A007583(n).

Extensions

Name clarified by David A. Corneth, Apr 15 2018