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A014916 a(1)=1, a(n) = n*4^(n-1) + a(n-1). 10
1, 9, 57, 313, 1593, 7737, 36409, 167481, 757305, 3378745, 14913081, 65244729, 283348537, 1222872633, 5249404473, 22429273657, 95443717689, 404681363001, 1710351420985, 7207909559865, 30297653743161, 127054676987449 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (9,-24,16).

FORMULA

a(n) = (1/9)*(1 + 4^n*(3*n-1)). - Paolo P. Lava, Jan 13 2009

a(1)=1, a(2)=9, a(n) = 8*a(n-1) - 16*a(n-2) + 1. - Vincenzo Librandi, Oct 23 2012

G.f.: x/((1-x)*(1-4*x)^2). - Vincenzo Librandi, Oct 23 2012

MAPLE

a:=n->sum (4^n-4^j, j=0..n): seq(a(n)/3, n=1..31); # Zerinvary Lajos, Dec 14 2008

MATHEMATICA

Join[{a=1, b=9}, Table[c=8*b-16*a+1; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Feb 07 2011 *)

CoefficientList[Series[1/((1 - x)(1 - 4*x)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 23 2012 *)

LinearRecurrence[{9, -24, 16}, {1, 9, 57}, 30] (* Harvey P. Dale, Jul 25 2015 *)

PROG

(MAGMA) I:=[1, 9]; [n le 2 select I[n] else 8*Self(n-1)-16*Self(n-2)+ 1: n in [1..30]]; // Vincenzo Librandi, Oct 23 2012

CROSSREFS

Sequence in context: A027210 A192054 A045720 * A045635 A026896 A080961

Adjacent sequences:  A014913 A014914 A014915 * A014917 A014918 A014919

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified October 27 12:59 EDT 2021. Contains 348276 sequences. (Running on oeis4.)