A017245 a(n) = 9*n + 7.

7, 16, 25, 34, 43, 52, 61, 70, 79, 88, 97, 106, 115, 124, 133, 142, 151, 160, 169, 178, 187, 196, 205, 214, 223, 232, 241, 250, 259, 268, 277, 286, 295, 304, 313, 322, 331, 340, 349, 358, 367, 376, 385, 394, 403, 412, 421, 430, 439, 448, 457, 466, 475, 484

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Numbers whose digital root is 7. - Halfdan Skjerning, Mar 15 2018

Links

• Tanya Khovanova, Recursive Sequences
• J. Laroche and N. J. A. Sloane, Correspondence, 1977
• Leo Tavares, Illustration: Triple Triangular Frames
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A008591, A017233.

Programs

Magma

[9*n+7: n in [0..60]]; // Vincenzo Librandi, Apr 30 2015

Mathematica

Range[7, 1000, 9] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *)
Table[9 n + 7, {n, 0, 70}] (* or *) CoefficientList[Series[(7 + 2 x)/(1 - x)^2, {x, 0, 60}], x] (* Vincenzo Librandi, Apr 30 2015 *)
LinearRecurrence[{2,-1},{7,16},60] (* Harvey P. Dale, Jul 30 2024 *)

PARI

vector(100,n,9*n-2) \\ Derek Orr, Apr 30 2015

Formula

a(n)^2 = A156676(n+1) + A017137(n). - Reinhard Zumkeller, Jul 13 2010

From Vincenzo Librandi, Apr 30 2015: (Start)

G.f.: (7+2*x)/(1-x)^2.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>2. (End)

E.g.f.: exp(x)*(7 + 9*x). - Stefano Spezia, Dec 08 2024