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
Links
- David Lovler, Table of n, a(n) for n = 1..10000
- Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
Programs
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Magma
[n: n in [1..500] | n mod 16 in [2, 3]]; // Vincenzo Librandi, Nov 30 2018
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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 *) -
PARI
a(n) = (16*n - 7*(-1)^n - 19)/2 \\ David Lovler, Aug 20 2022
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