A249993 Expansion of 1/((1+x)*(1+2*x)*(1-4*x)).

1, 1, 11, 29, 147, 525, 2227, 8653, 35123, 139469, 559923, 2235597, 8950579, 35785933, 143176499, 572640461, 2290692915, 9162509517, 36650562355, 146601200845, 586406900531, 2345623407821, 9382502019891, 37529991302349, 150119998763827, 600479927946445

Offset: 0

Author

Alex Ratushnyak, Dec 27 2014

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (1,10,8).

Crossrefs

Cf. A249992.

Cf. A006095, A171477 for g.f. 1/((1-x)*(1-2*x)*(1-4*x)).

Cf. A015249, A084152, A084175 for g.f. 1/((1-x)*(1+2*x)*(1-4*x)).

Cf. A109765 for g.f. 1/((1+x)*(1-2*x)*(1-4*x)).

Programs

Magma

[(2^(2*n+3) +(-1)^n*(5*2^(n+1)-3))/15: n in [0..40]]; // G. C. Greubel, Oct 10 2022

Mathematica

CoefficientList[Series[1/((1+x)(1+2x)(1-4x)),{x,0,30}],x] (* or *) LinearRecurrence[{1,10,8},{1,1,11},30] (* Harvey P. Dale, Dec 13 2018 *)

PARI

Vec(1/((1+x)*(1+2*x)*(1-4*x)) + O(x^40)) \\ Michel Marcus, Dec 28 2014

SageMath

[(2^(2*n+3) +(-1)^n*(5*2^(n+1)-3))/15 for n in range(41)] # G. C. Greubel, Oct 10 2022

Formula

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

a(n) = ( 2^(3+2*n) + (5*2^(1+n) - 3)*(-1)^n )/15. Colin Barker, Dec 28 2014

a(n) = a(n-1) + 10*a(n-2) + 8*a(n-3). - Colin Barker, Dec 28 2014

E.g.f.: (1/15)*(10*exp(-2*x) - 3*exp(-x) + 8*exp(4*x)). - G. C. Greubel, Oct 10 2022