A088578 a(n) = n*x^n + (n-1)*x^(n-1) + . . . + x + 1 for x=2.

1, 3, 11, 35, 99, 259, 643, 1539, 3587, 8195, 18435, 40963, 90115, 196611, 425987, 917507, 1966083, 4194307, 8912899, 18874371, 39845891, 83886083, 176160771, 369098755, 771751939, 1610612739, 3355443203, 6979321859, 14495514627, 30064771075, 62277025795

Offset

0,2

Comments

For x=1 this is A000124.

Equals row sums of triangle A144332. Left border of A144332 = A000124. - Gary W. Adamson, Sep 18 2008

Links

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

Index entries for linear recurrences with constant coefficients, signature (5,-8,4).

Formula

a(n) = (n-1) * 2^(n+1) + 3.

a(n) = 5*a(n-1) - 8*a(n-2) + 4*a(n-3). - Colin Barker, Apr 02 2012

G.f.: (1-2*x+4*x^2)/((1-x)*(1-2*x)^2). - Colin Barker, Apr 02 2012

Example

Sum of reciprocals = 1.469480896985753544533086291..

Mathematica

LinearRecurrence[{5, -8, 4}, {1, 3, 11}, 40] (* Harvey P. Dale, Dec 22 2013 *)
Table[(n - 1) 2^(n + 1) + 3, {n, 0, 30}] (* Vincenzo Librandi, Jun 14 2015 *)

Prog

(PARI) trajpolypn(n1, k) = { s=0; for(x1=1, 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((1-2*x+4*x^2)/((1-x)*(1-2*x)^2) + O(x^50)) \\ Colin Barker, Jun 13 2015
(Magma) I:=[1, 3, 11]; [n le 3 select I[n] else 5*Self(n-1)-8*Self(n-2)+4*Self(n-3): n in [1..35]]; // Vincenzo Librandi, Jun 14 2015

Crossrefs

Cf. A000124.

Cf. A144332.

Sequence in context: A094308 A166046 A223626 * A320683 A027060 A171498

Adjacent sequences: A088575 A088576 A088577 * A088579 A088580 A088581

Keyword

nonn,easy

Author

Cino Hilliard, Nov 20 2003

Status

approved