A166754 a(n) = 4*A061547(n+1) - 3*A166753(n).

1, 2, 9, 22, 53, 114, 241, 494, 1005, 2026, 4073, 8166, 16357, 32738, 65505, 131038, 262109, 524250, 1048537, 2097110, 4194261, 8388562, 16777169, 33554382, 67108813, 134217674, 268435401, 536870854, 1073741765, 2147483586

Offset: 0

Author

Paul Barry, Oct 21 2009

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,2).

Crossrefs

Cf. A061547, A166753.

Cf. A000975, A011377.

Programs

GAP

List([0..40], n-> (2^(n+3) + (-1)^n - (4*n+7))/2) # G. C. Greubel, Jun 04 2019

Magma

[(2^(n+3) +(-1)^n -(4*n+7))/2: n in [0..40]]; // G. C. Greubel, Oct 10 2017

Mathematica

LinearRecurrence[{3,-1,-3,2}, {1,2,9,22}, 40] (* G. C. Greubel, May 24 2016 *)

PARI

my(x='x+O('x^40)); Vec((1-x+4*x^2)/((1+x)*(1-x)^2*(1-2*x))) \\ G. C. Greubel, Oct 10 2017

Sage

[(2^(n+3) + (-1)^n - (4*n+7))/2 for n in (0..40)] # G. C. Greubel, Jun 04 2019

Formula

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

a(n) = (2^(n+3) + (-1)^n - (4*n+7))/2.

a(n) = A000975(n) - 4*A011377(n-2).

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

E.g.f.: (8*exp(2*x) + exp(-x) - (4*x+7)*exp(x))/2. - G. C. Greubel, Jun 04 2019