A122709 a(0)=1; thereafter a(n) = 9*n - 3.

1, 6, 15, 24, 33, 42, 51, 60, 69, 78, 87, 96, 105, 114, 123, 132, 141, 150, 159, 168, 177, 186, 195, 204, 213, 222, 231, 240, 249, 258, 267, 276, 285, 294, 303, 312, 321, 330, 339, 348, 357, 366, 375, 384, 393, 402, 411, 420, 429, 438, 447, 456, 465, 474, 483

Offset: 0

Author

Philippe Deléham, Sep 23 2006

Keywords

• nonn
• easy

Comments

Self-convolution of A122553.

Links

• Colin Barker, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A017233 (9n+6), A008591, A122553.

Programs

GAP

a:=[6,15];; for n in [3..60] do a[n]:=2*a[n-1]-a[n-2]; od; Concatenation([1],a); # Muniru A Asiru, Oct 21 2018

Maple

seq(coeff(series(((1+2*x)/(1-x))^2,x,n+1), x, n), n = 0 .. 60); # Muniru A Asiru, Oct 21 2018

Mathematica

Join[{1},LinearRecurrence[{2,-1},{6,15},60]] (* Harvey P. Dale, Jun 12 2012 *)

PARI

a(n)=max(9*n-3,1) \\ Charles R Greathouse IV, Jan 17 2012

PARI

Vec((1 + 2*x)^2 / (1 - x)^2 + O(x^100)) \\ Colin Barker, Jan 22 2018

Formula

a(0)=1, a(n) = 9*n - 3 = A008591(n) - 3 for n > 0.

a(n) = 2*a(n-1) - a(n-2) for n > 2; a(0)=1, a(1)=6, a(2)=15.

a(n) = a(n-1) + 9 for n > 1; a(0)=1, a(1)=6.

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

Equals binomial transform of [1, 5, 4, -4, 4, -4, 4, ...]. - Gary W. Adamson, Dec 10 2007

a(n) = A017233(n-1) for n > 0. - Georg Fischer, Oct 21 2018

E.g.f.: exp(x)*(9*x - 3) + 4. - Stefano Spezia, Mar 07 2023

Extensions

Edited by N. J. A. Sloane, Jan 23 2018