A017533 a(n) = 12*n + 1.

1, 13, 25, 37, 49, 61, 73, 85, 97, 109, 121, 133, 145, 157, 169, 181, 193, 205, 217, 229, 241, 253, 265, 277, 289, 301, 313, 325, 337, 349, 361, 373, 385, 397, 409, 421, 433, 445, 457, 469, 481, 493, 505, 517, 529, 541, 553, 565, 577, 589, 601, 613, 625, 637

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A161700, A005408, A016813, A016921, A017281, A158057, A161705, A161709, A161714, A128470, A016945, A287326 (third column).

Programs

C

#include
int main(){
int n;
for(n=0; n<=100; n++)
printf("%d, ", 12*n + 1);
return 0;
} /* Indranil Ghosh, Apr 05 2017 */

GAP

List([0..60], n-> 12*n + 1); # G. C. Greubel, Sep 18 2019

Magma

[12*n+1: n in [0..60]]; // G. C. Greubel, Sep 18 2019

Maple

seq(12*n+1, n=0..60); # G. C. Greubel, Sep 18 2019

Mathematica

Array[12*#+1&,60,0] (* Vladimir Joseph Stephan Orlovsky, Dec 14 2009 *)
CoefficientList[Series[(1+11x)/(1-x)^2, {x, 0,60}], x] (* Michael De Vlieger, Apr 05 2017 *)

PARI

a(n)=12*n+1 \\ Charles R Greathouse IV, Jul 10 2016

Python

def a(n): return 12*n + 1 # Indranil Ghosh, Apr 05 2017

Sage

[12*n + 1 for n in (0..60)] # G. C. Greubel, Sep 18 2019

Formula

a(n) = 12*n + 1, n >= 0.

a(n) = 24*n - 10 - a(n-1), (with a(0)=1). - Vincenzo Librandi, Dec 24 2010

G.f.: (1 + 11*x)/(1-x)^2. - Indranil Ghosh, Apr 05 2017

E.g.f.: (1 + 12*x)*exp(x). - G. C. Greubel, Sep 18 2019