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A175885
Numbers that are congruent to {1, 10} mod 11.
18
1, 10, 12, 21, 23, 32, 34, 43, 45, 54, 56, 65, 67, 76, 78, 87, 89, 98, 100, 109, 111, 120, 122, 131, 133, 142, 144, 153, 155, 164, 166, 175, 177, 186, 188, 197, 199, 208, 210, 219, 221, 230, 232, 241, 243, 252, 254, 263, 265, 274, 276, 285, 287, 296, 298
OFFSET
1,2
COMMENTS
Cf. property described by Gary Detlefs in A113801: more generally, these numbers are of the form (2*h*n + (h-4)*(-1)^n - h)/4 (h, n natural numbers), therefore ((2*h*n + (h-4)*(-1)^n - h)/4)^2 - 1 == 0 (mod h); in this case, a(n)^2 - 1 == 0 (mod 11).
FORMULA
G.f.: x*(1+9*x+x^2)/((1+x)*(1-x)^2).
a(n) = (22*n + 7*(-1)^n - 11)/4.
a(n) = -a(-n+1) = a(n-2) + 11 = a(n-1) + a(n-2) - a(n-3).
a(n) = 11*A000217(n-1) + 1 - 2*Sum_{i=1..n-1} a(i) for n > 1.
a(n) = A195312(n) + A195312(n-1) = A195313(n) - A195313(n-2). - Bruno Berselli, Sep 18 2011
Sum_{n>=1} (-1)^(n+1)/a(n) = (Pi/11)*cot(Pi/11). - Amiram Eldar, Dec 04 2021
E.g.f.: 1 + ((22*x - 11)*exp(x) + 7*exp(-x))/4. - David Lovler, Sep 04 2022
MATHEMATICA
Rest[Flatten[{#-1, #+1}&/@(11 Range[0, 50])]] (* Harvey P. Dale, Nov 05 2010 *)
PROG
(Magma) [(22*n+7*(-1)^n-11)/4: n in [1..60]]; // Vincenzo Librandi, Sep 19 2011
(Haskell)
a175885 n = a175885_list !! (n-1)
a175885_list = 1 : 10 : map (+ 11) a175885_list
-- Reinhard Zumkeller, Jan 07 2012
(PARI) a(n)=n%2*9 + 1 \\ Charles R Greathouse IV, Aug 01 2016
CROSSREFS
Cf. A090771 (n==1 or 9 mod 10), A091998 (n==1 or 11 mod 12).
Cf. A195043 (partial sums).
Sequence in context: A108965 A366958 A341002 * A061870 A348056 A120001
KEYWORD
nonn,easy
AUTHOR
Bruno Berselli, Oct 08 2010 - Nov 17 2010
STATUS
approved