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 A195817 Multiples of 10 and odd numbers interleaved. 19
 0, 1, 10, 3, 20, 5, 30, 7, 40, 9, 50, 11, 60, 13, 70, 15, 80, 17, 90, 19, 100, 21, 110, 23, 120, 25, 130, 27, 140, 29, 150, 31, 160, 33, 170, 35, 180, 37, 190, 39, 200, 41, 210, 43, 220, 45, 230, 47, 240, 49, 250, 51, 260, 53, 270, 55, 280, 57, 290, 59, 300 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A008592 and A005408 interleaved. Partial sums give the generalized 14-gonal (or tetradecagonal) numbers A195818. a(n) is also the length of the n-th line segment of a rectangular spiral on the infinite square grid. The vertices of the spiral are the generalized 14-gonal numbers. - Omar E. Pol, Jul 27 2018 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..10000 Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1). FORMULA a(n) = (2*(-1)^n+3)*n. - Vincenzo Librandi, Sep 30 2011 From Bruno Berselli, Sep 30 2011: (Start) G.f.: x*(1+10*x+x^2))/((1-x)^2*(1+x)^2). a(n) = -a(-n) = a(n-2)*n/(n-2) = 2*a(n-2)-a(n-4). a(n) * a(n+1) = a(n(n+1)). a(n) + a(n+1) = A091998(n+1). (End) a(0)=0, a(1)=1, a(2)=10, a(3)=3, a(n)=2*a(n-2)-a(n-4). - Harvey P. Dale, Nov 24 2013 Multiplicative with a(2^e) = 5*2^e, a(p^e) = p^e for odd prime p. - Andrew Howroyd, Jul 23 2018 MATHEMATICA With[{nn=30}, Riffle[10*Range[0, nn], Range[1, 2*nn+1, 2]]] (* or *) LinearRecurrence[{0, 2, 0, -1}, {0, 1, 10, 3}, 70] (* Harvey P. Dale, Nov 24 2013 *) PROG (Magma) [(2*(-1)^n+3)*n: n in [0..60]]; // Vincenzo Librandi, Sep 30 2011 (PARI) a(n) = (2*(-1)^n+3)*n; \\ Andrew Howroyd, Jul 23 2018 CROSSREFS Column 10 of A195151. Sequences whose partial sums give the generalized n-gonal numbers, if n>=5: A026741, A001477, zero together with A080512, A022998, A195140, zero together with A165998, A195159, A195161, A195312, this sequence. Cf. A195152. Sequence in context: A050133 A068608 A358278 * A347126 A228314 A243239 Adjacent sequences: A195814 A195815 A195816 * A195818 A195819 A195820 KEYWORD nonn,easy,mult AUTHOR Omar E. Pol, Sep 29 2011 STATUS approved

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Last modified January 30 04:55 EST 2023. Contains 359939 sequences. (Running on oeis4.)