A280014 Numbers m == +- 2 (mod 10) but not m == 2 (mod 6).

12, 18, 22, 28, 42, 48, 52, 58, 72, 78, 82, 88, 102, 108, 112, 118, 132, 138, 142, 148, 162, 168, 172, 178, 192, 198, 202, 208, 222, 228, 232, 238, 252, 258, 262, 268, 282, 288, 292, 298, 312, 318, 322, 328, 342, 348, 352, 358, 372, 378, 382, 388, 402, 408, 412, 418, 432, 438, 442, 448, 462, 468, 472, 478, 492, 498, 502, 508, 522

Offset: 1

Author

M. F. Hasler, Feb 21 2017

Keywords

• nonn
• easy

Comments

Also, numbers congruent to 12, 18, 22 or 28 (mod 30). Also, numbers such that A056619(n) = 5.

Links

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

Crossrefs

Cf. A056619, A057077.

Programs

Mathematica

Select[Range@ 524, MemberQ[{12, 18, 22, 28}, Mod[#, 30]] &] (* Michael De Vlieger, Feb 21 2017 *)
LinearRecurrence[{1,0,0,1,-1},{12,18,22,28,42},80] (* Harvey P. Dale, Nov 09 2017 *)

PARI

a(n)=[12,18,22,28][(n-1)%4+1]+(n-1)\4*30

PARI

Vec(2*x*(2 + x)*(3 + x^2 + x^3) / ((1 - x)^2*(1 + x)*(1 + x^2)) + O(x^60)) \\ Colin Barker, Feb 12 2018

Formula

a(n+4) = a(n)+30.

From Colin Barker, Feb 12 2018: (Start)

G.f.: 2*x*(2 + x)*(3 + x^2 + x^3) / ((1 - x)^2*(1 + x)*(1 + x^2)).

a(n) = a(n-1) + a(n-4) - a(n-5) for n>5.

(End)

a(n) = (5 + 30*n - 3*(-1)^n + 10*A057077(n))/4. - Stefano Spezia, Dec 26 2021