A321212 Numbers that are congruent to {2, 3} mod 16.

2, 3, 18, 19, 34, 35, 50, 51, 66, 67, 82, 83, 98, 99, 114, 115, 130, 131, 146, 147, 162, 163, 178, 179, 194, 195, 210, 211, 226, 227, 242, 243, 258, 259, 274, 275, 290, 291, 306, 307, 322, 323, 338, 339, 354, 355, 370, 371, 386, 387, 402, 403, 418, 419, 434, 435, 450, 451, 466, 467, 482, 483, 498, 499

Offset

1,1

Links

David Lovler, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Formula

a(n) = A151977(n) + 2.

G.f.: x*(2 + x + 13*x^2)/((-1 + x)^2*(1 + x)). - Stefano Spezia, Nov 01 2018

a(n) = a(n-1) + a(n-2) - a(n-3) for n > 3. - Chai Wah Wu, Nov 29 2018

From Franck Maminirina Ramaharo, Nov 30 2018: (Start)

a(n) = (16*n - 7*(-1)^n - 19)/2.

E.g.f.: (-7 + 26*exp(x) - 19*exp(2*x) + 16*x*exp(2*x))/(2*exp(x)). (End)

E.g.f.: 13 + ((16*x -19)*exp(x) - 7*exp(-x))/2. - David Lovler, Aug 20 2022

a(n) = a(n-2) + 16. - David A. Corneth, Nov 30 2018

Mathematica

Flatten@ Array[16 # + {2, 3} &, 31, 0] (* Michael De Vlieger, Oct 31 2018 *)
Select[Range[1, 500], MemberQ[{2, 3}, Mod[#, 16]] &] (* Vincenzo Librandi, Nov 30 2018 *)

Prog

(Magma) [n: n in [1..500] | n mod 16 in [2, 3]]; // Vincenzo Librandi, Nov 30 2018
(PARI) a(n) = (16*n - 7*(-1)^n - 19)/2 \\ David Lovler, Aug 20 2022

Crossrefs

Cf. A047608, A151977.

A091968 is a subsequence.

Sequence in context: A328624 A328627 A032808 * A037317 A112664 A216890

Adjacent sequences: A321209 A321210 A321211 * A321213 A321214 A321215

Keyword

nonn,easy

Author

Yuen Biu, Oct 31 2018

Status

approved