A321421 a(n) = 10*(4^n - 1)/3 + 1.

1, 11, 51, 211, 851, 3411, 13651, 54611, 218451, 873811, 3495251, 13981011, 55924051, 223696211, 894784851, 3579139411, 14316557651, 57266230611, 229064922451, 916259689811, 3665038759251, 14660155037011, 58640620148051, 234562480592211, 938249922368851

Offset: 0

Author

Paul Curtz, Nov 09 2018

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (5,-4).

Crossrefs

Cf. A000302, A002450, A010727.

Programs

GAP

List([0..25],n->10*(4^n-1)/3+1); # Muniru A Asiru, Nov 10 2018

Maple

seq(coeff(series((1+6*x)/((1-x)*(1-4*x)),x,n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Nov 10 2018

Mathematica

a[n_]:=10*(4^n - 1)/3 + 1 ; Array[a, 20, 0] (* or *)
CoefficientList[Series[-((7 E^x)/3) + (10 E^(4 x))/3 , {x, 0, 20}], x]*Table[n!, {n, 0, 20}] (* Stefano Spezia, Nov 10 2018 *)
LinearRecurrence[{5,-4},{1,11},30] (* Harvey P. Dale, Aug 22 2020 *)

PARI

Vec((1 + 6*x) / ((1 - x)*(1 - 4*x)) + O(x^30)) \\ Colin Barker, Nov 10 2018

Formula

a(n) = 4*a(n-1) + 7, a(0) = 1 for n > 0.

a(n) = 5*a(n-1) - 4*a(n-2), a(0) = 1, a(1) = 11, n > 1.

a(n) = a(n-1) + 10*4^(n-1), a(0) = 1, n > 0.

a(n) = A086462(n) + 1 for n > 0. - Michel Marcus, Nov 09 2018

G.f.: (1 + 6*x) / ((1 - x)*(1 - 4*x)). - Colin Barker, Nov 10 2018

E.g.f.: (-7*exp(x) + 10*exp(4*x))/3. - Stefano Spezia, Nov 10 2018

a(n) = 10*A002450(n) + 1. - Omar E. Pol, Nov 10 2018

Extensions

More terms from Colin Barker, Nov 10 2018