A084213 Binomial transform of A081250.

1, 4, 18, 76, 312, 1264, 5088, 20416, 81792, 327424, 1310208, 5241856, 20969472, 83881984, 335536128, 1342160896, 5368676352, 21474770944, 85899214848, 343597121536, 1374389010432, 5497557090304, 21990230458368, 87960926027776

Offset

0,2

Comments

When 5*2^n - 1 is prime, that is, n is in A001770, then a(n+1) is in A136539. - Farideh Firoozbakht and M. F. Hasler, Nov 03 2012

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..400

Index entries for linear recurrences with constant coefficients, signature (6,-8)

Formula

a(n) = (5*4^n - 2^(n+1) + 0^n)/4.

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

E.g.f.: (5*exp(4*x) - 2*exp(2*x) + 1)/4.

a(n+1) = 2^n*(5*2^n - 1) for all n >= 0. - M. F. Hasler, Nov 03 2012

Maple

seq(coeff(series((1-2*x+2*x^2)/((1-2*x)*(1-4*x)), x, n+1), x, n), n = 0 .. 25); # Muniru A Asiru, Oct 09 2018

Mathematica

Table[If[n==0, 1, 2^(n-2)*(5*2^n - 2)], {n, 0, 30}] (* G. C. Greubel, Oct 08 2018 *)
CoefficientList[Series[(1 - 2*x + 2*x^2)/((1-2*x)*(1-4*x)), {x, 0, 50}], x] (* or *)
CoefficientList[Series[(5*Exp[4*x] - 2*Exp[2*x] + 1)/4, {x, 0, 50}], x]*Table[k!, {k, 0, 50}] (* Stefano Spezia, Oct 11 2018 *)

Prog

(Magma) [5*4^n/4-2^n/2+0^n/4: n in [0..30]]; // Vincenzo Librandi, Jun 15 2011
(PARI) vector(30, n, n--; (5*4^n - 2^(n+1) + 0^n)/4) \\ G. C. Greubel, Oct 08 2018

Crossrefs

Sequence in context: A037674 A066259 A172159 * A048664 A108012 A291417

Adjacent sequences: A084210 A084211 A084212 * A084214 A084215 A084216

Keyword

easy,nonn

Author

Paul Barry, May 19 2003

Status

approved