A014831 a(1)=1; for n>1, a(n) = 8*a(n-1)+n.

1, 10, 83, 668, 5349, 42798, 342391, 2739136, 21913097, 175304786, 1402438299, 11219506404, 89756051245, 718048409974, 5744387279807, 45955098238472, 367640785907793, 2941126287262362, 23529010298098915, 188232082384791340, 1505856659078330741

Offset

1,2

Links

Colin Barker, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (10,-17,8).

Formula

a(n) = (8^(n+1)-7*n-8)/49. - Rolf Pleisch, Oct 21 2010

a(n) = Sum_{i=0..n-1} 7^i*binomial(n+1,n-1-i). [Bruno Berselli, Nov 13 2015]

From Colin Barker, Jun 03 2020: (Start)

G.f.: x / ((1 - x)^2*(1 - 8*x)).

a(n) = 10*a(n-1) - 17*a(n-2) + 8*a(n-3) for n>3.

(End)

Example

For n=5, a(5) = 1*15 + 7*20 + 7^2*15 + 7^3*6 + 7^4*1 = 5349. [Bruno Berselli, Nov 13 2015]

Maple

a:=n->sum((8^(n-j)-1)/7, j=0..n): seq(a(n), n=1..19); # Zerinvary Lajos, Jan 15 2007
a:= n-> (Matrix ([[1, 0, 1], [1, 1, 1], [0, 0, 8]])^n)[2, 3]: seq (a(n), n=1..25); # Alois P. Heinz, Aug 06 2008

Mathematica

Table[(8^(n + 1) - 7 n - 8)/49, {n, 1, 25}] (* Bruno Berselli, Nov 13 2015 *)

Prog

(PARI) Vec(x / ((1 - x)^2*(1 - 8*x)) + O(x^25)) \\ Colin Barker, Jun 03 2020

Crossrefs

Cf. A000420, A104712.

Sequence in context: A037699 A037608 A055149 * A048440 A226202 A271557

Adjacent sequences: A014828 A014829 A014830 * A014832 A014833 A014834

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved