A014830 a(1)=1; for n > 1, a(n) = 7*a(n-1) + n.

1, 9, 66, 466, 3267, 22875, 160132, 1120932, 7846533, 54925741, 384480198, 2691361398, 18839529799, 131876708607, 923136960264, 6461958721864, 45233711053065, 316635977371473, 2216451841600330

Offset

1,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (9,-15,7).

Formula

a(n) = (7^(n+1) - 6*n - 7)/36. - Rolf Pleisch, Oct 19 2010

a(1)=1, a(2)=9, a(3)=66; for n > 3, a(n) = 9*a(n-1) - 15*a(n-2) + 7*a(n-3). - Harvey P. Dale, Jul 22 2013

a(n) = Sum_{i=0..n-1} 6^i*binomial(n+1,n-1-i). - Bruno Berselli, Nov 13 2015

G.f.: x / ((1 - x)^2*(1 - 7*x)). - Colin Barker, Jun 03 2020

Example

For n=5, a(5) = 1*15 + 6*20 + 6^2*15 + 6^3*6 + 6^4*1 = 3267. - Bruno Berselli, Nov 13 2015

Maple

a:=n->sum((7^(n-j)-1)/6, j=0..n): seq(a(n), n=1..19); # Zerinvary Lajos, Jan 15 2007

Mathematica

a[1] = 1; a[n_] := 7*a[n-1]+n; Table[a[n], {n, 10}] (* Zak Seidov, Feb 06 2011 *)
LinearRecurrence[{9, -15, 7}, {1, 9, 66}, 30] (* Harvey P. Dale, Jul 22 2013 *)

Prog

(PARI) Vec(x / ((1 - x)^2*(1 - 7*x)) + O(x^25)) \\ Colin Barker, Jun 03 2020

Crossrefs

Cf. A000400, A104712.

Sequence in context: A037698 A037607 A055148 * A048439 A134432 A098107

Adjacent sequences: A014827 A014828 A014829 * A014831 A014832 A014833

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved