A139619 a(n) = 171*n + 19.

19, 190, 361, 532, 703, 874, 1045, 1216, 1387, 1558, 1729, 1900, 2071, 2242, 2413, 2584, 2755, 2926, 3097, 3268, 3439, 3610, 3781, 3952, 4123, 4294, 4465, 4636, 4807, 4978, 5149, 5320, 5491, 5662, 5833, 6004, 6175, 6346, 6517, 6688

Offset: 0

Author

Omar E. Pol, May 21 2008

Keywords

• easy
• nonn

Comments

Numbers of the 19th column of positive numbers in the square array of nonnegative and polygonal numbers A139600. Also, numbers of the 19th column in the square array A057145.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A016957, A017329, A057145, A139600, A139606-A139618, A139620.

Cf. A017173, A051682.

Programs

Magma

[19*(9*n + 1): n in [0..50]]; // Vincenzo Librandi, Jul 23 2011

Mathematica

Range[0, 100]*171 + 19 (* Paolo Xausa, Apr 17 2024 *)

PARI

a(n)=171*n+19 \\ Charles R Greathouse IV, Oct 05 2011

Formula

From Chai Wah Wu, Apr 14 2017: (Start)

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

G.f.: (152*x + 19)/(x - 1)^2. (End)

From Elmo R. Oliveira, Apr 11 2024: (Start)

E.g.f.: 19*exp(x)*(1 + 9*x).

a(n) = 19*A017173(n) = 19*(A051682(n+1) - A051682(n)). (End)