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 A017629 a(n) = 12*n + 9. 20
 9, 21, 33, 45, 57, 69, 81, 93, 105, 117, 129, 141, 153, 165, 177, 189, 201, 213, 225, 237, 249, 261, 273, 285, 297, 309, 321, 333, 345, 357, 369, 381, 393, 405, 417, 429, 441, 453, 465, 477, 489, 501, 513, 525, 537, 549, 561, 573, 585, 597, 609, 621, 633 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Numbers k such that k mod 2 = (k+1) mod 3 = 1 and (k+2) mod 4 != 1. - Klaus Brockhaus, Jun 15 2004 For n > 3, the number of squares on the infinite 3-column chessboard at <= n knight moves from any fixed point. - Ralf Stephan, Sep 15 2004 A016946 is the subsequence of squares (for n = 3*k*(k+1) = A028896(k), then a(n) = (6k+3)^2 = A016946(k)). - Bernard Schott, Apr 05 2021 LINKS Table of n, a(n) for n=0..52. Tanya Khovanova, Recursive Sequences. Index entries for linear recurrences with constant coefficients, signature (2,-1). FORMULA a(n) = 6*(4*n+1) - a(n-1) (with a(0)=9). - Vincenzo Librandi, Dec 17 2010 A089911(2*a(n)) = 4. - Reinhard Zumkeller, Jul 05 2013 G.f.: (9 + 3*x)/(1 - x)^2. - Alejandro J. Becerra Jr., Jul 08 2020 Sum_{n>=0} (-1)^n/a(n) = (Pi + log(3-2*sqrt(2)))/(12*sqrt(2)). - Amiram Eldar, Dec 12 2021 E.g.f.: 3*exp(x)*(3 + 4*x). - Stefano Spezia, Feb 25 2023 MATHEMATICA 12*Range[0, 200]+9 (* Vladimir Joseph Stephan Orlovsky, Feb 19 2011 *) LinearRecurrence[{2, -1}, {9, 21}, 60] (* Harvey P. Dale, Apr 14 2019 *) PROG (Sage) [i+9 for i in range(525) if gcd(i, 12) == 12] # Zerinvary Lajos, May 21 2009 (Haskell) a017629 = (+ 9) . (* 12) -- Reinhard Zumkeller, Jul 05 2013 (PARI) a(n)=12*n+9 \\ Charles R Greathouse IV, Jul 10 2016 CROSSREFS Subsequences include A072065, A016945, A016813, A008585, and A005408. Cf. A008594, A017533, A017545, A017137, A004767, A001019, A028896, A016946, A089911. Sequence in context: A325573 A086470 A176256 * A216240 A176258 A107978 Adjacent sequences: A017626 A017627 A017628 * A017630 A017631 A017632 KEYWORD nonn,easy AUTHOR N. J. A. Sloane STATUS approved

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Last modified September 10 21:37 EDT 2024. Contains 375795 sequences. (Running on oeis4.)