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A305859 Numbers that are congruent to {1, 3, 11} mod 12. 0
1, 3, 11, 13, 15, 23, 25, 27, 35, 37, 39, 47, 49, 51, 59, 61, 63, 71, 73, 75, 83, 85, 87, 95, 97, 99, 107, 109, 111, 119, 121, 123, 131, 133, 135, 143, 145, 147, 155, 157, 159, 167, 169, 171, 179, 181, 183, 191, 193, 195, 203, 205, 207, 215, 217, 219, 227, 229, 231, 239 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
FORMULA
G.f.: x*(1 + 2*x + 8*x^2 + x^3)/((1 - x)^2*(1 + x + x^2)).
a(n) = a(n-1) + a(n-3) - a(n-4) for n>12.
a(n) = 2*a(n-1) - 2*a(n-2) + 2*a(n-3) - 2*a(n-4) + 2*a(n-5) - a(n-6) for n>6.
a(n) = 2*n + 6*floor(n/3) - 1. - Bruno Berselli, Jun 13 2018
MATHEMATICA
Table[2 n + 6 Floor[n/3] - 1, {n, 1, 60}] (* Bruno Berselli, Jun 13 2018 *)
LinearRecurrence[{1, 0, 1, -1}, {1, 3, 11, 13}, 60] (* Harvey P. Dale, Mar 15 2023 *)
PROG
(Magma) [n: n in [0..300] | n mod 12 in [1, 3, 11]]; // Bruno Berselli, Jun 13 2018
CROSSREFS
Equals 2*A047240 - 1 and 2*A047266 + 1 (after 0).
Sequence in context: A119231 A177335 A031449 * A090260 A179522 A020635
KEYWORD
nonn,easy,less
AUTHOR
Vincenzo Librandi, Jun 12 2018
EXTENSIONS
Edited by Bruno Berselli, Jun 13 2018
STATUS
approved

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Last modified February 23 09:02 EST 2024. Contains 370276 sequences. (Running on oeis4.)