A274638 Main diagonal of A274637.

0, 0, 3, 5, 15, 27, 63, 119, 255, 495, 1023, 2015, 4095, 8127, 16383, 32639, 65535, 130815, 262143, 523775, 1048575, 2096127, 4194303, 8386559, 16777215, 33550335, 67108863, 134209535, 268435455, 536854527, 1073741823, 2147450879, 4294967295, 8589869055, 17179869183, 34359607295, 68719476735

Offset: 0

Author

N. J. A. Sloane, Jul 08 2016

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,0,-6,4).

Crossrefs

Cf. A274637.

Programs

Mathematica

LinearRecurrence[{3, 0, -6, 4}, {0, 0, 3, 5}, 50] (* Paolo Xausa, Oct 21 2024 *)

PARI

concat([0,0], Vec(x^2*(3-4*x)/((1-x)*(1-2*x)*(1-2*x^2)) + O(x^40))) \\ Colin Barker, Jul 09 2016

Formula

From Colin Barker, Jul 09 2016: (Start)

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

a(n) = 2^n-1 for n even.

a(n) = 2^n-1-2^((n-1)/2) for n odd.

a(n) = 3*a(n-1)-6*a(n-3)+4*a(n-4) for n>3.

G.f.: x^2*(3-4*x) / ((1-x)*(1-2*x)*(1-2*x^2)).

(End)