A088582 a(n) = n*x^n + (n-1)*x^(n-1) + . . . + x + 1 for x=4.

1, 5, 37, 229, 1253, 6373, 30949, 145637, 669925, 3029221, 13514981, 59652325, 260978917, 1133394149, 4891490533, 20997617893, 89717094629, 381774870757, 1618725452005, 6841405683941, 28831638239461, 121190614972645, 508218707949797, 2126699824036069

Offset

0,2

Comments

Sum of reciprocals = 1.232389931990837220821336083..

Links

Colin Barker, Table of n, a(n) for n = 0..1000

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

Formula

a(n) = (13+(3n-1)*4^(n+1))/9 = 9*a(n-1)-24*a(n-2)+16*a(n-3). G.f.: (1-4x+16x^2)/((1-x)(1-4x)^2). - R. J. Mathar, Jul 22 2009

Example

4*4^4 + 3*4^3 + 2*4^2 + 4 + 1 = 1253.

Mathematica

LinearRecurrence[{9, -24, 16}, {1, 5, 37}, 50] (* Vincenzo Librandi, Jun 14 2015 *)
CoefficientList[Series[(1-4x+16x^2)/((1-x)(1-4x)^2), {x, 0, 30}], x] (* Harvey P. Dale, Oct 13 2024 *)

Prog

(PARI) trajpolyn(n1, k) = { s=0; for(x1=0, n1, y1 = polypn2(k, x1); print1(y1", "); s+=1.0/y1; ); print(); print(s) }
polypn2(n, p) = { x=n; y=1; for(m=1, p, y=y+m*x^m; ); return(y) }
(PARI) Vec(-(16*x^2-4*x+1)/((x-1)*(4*x-1)^2) + O(x^100)) \\ Colin Barker, Jun 13 2015
(Magma) [(13+(3*n-1)*4^(n+1))/9: n in [0..30]]; // Vincenzo Librandi, Jun 14 2015

Crossrefs

Sequence in context: A179567 A362337 A339386 * A088583 A202556 A015548

Adjacent sequences: A088579 A088580 A088581 * A088583 A088584 A088585

Keyword

nonn,easy

Author

Cino Hilliard, Nov 20 2003

Extensions

Offset corrected by R. J. Mathar, Jul 22 2009

Status

approved