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 A195312 Multiples of 9 and odd numbers interleaved. 23
 0, 1, 9, 3, 18, 5, 27, 7, 36, 9, 45, 11, 54, 13, 63, 15, 72, 17, 81, 19, 90, 21, 99, 23, 108, 25, 117, 27, 126, 29, 135, 31, 144, 33, 153, 35, 162, 37, 171, 39, 180, 41, 189, 43, 198, 45, 207, 47, 216, 49, 225, 51, 234, 53, 243, 55, 252 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Partial sums give the generalized 13-gonal (or tridecagonal) numbers A195313. 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 13-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 From Bruno Berselli, Sep 15 2011:  (Start) G.f.: x*(1+9*x+x^2)/((1-x)^2*(1+x)^2). a(n) = (7*(-1)^n+11)*n/4. a(n) + a(n-1) = A175885(n). Sum_{i=0..n} a(i) = A195313(n). (End) Multiplicative with a(2^e) = 9*2^(e-1), a(p^e) = p^e for odd prime p. - Andrew Howroyd, Jul 23 2018 MATHEMATICA With[{nn=30}, Riffle[9Range[0, nn], Range[1, 2nn+1, 2]]] (* Harvey P. Dale, Sep 24 2011 *) PROG (MAGMA) /* By definition */ &cat[[9*n, 2*n+1]: n in [0..33]]; // Bruno Berselli, Sep 16 2011 (PARI) a(n)=(7*(-1)^n+11)*n/4 \\ Charles R Greathouse IV, Oct 07 2015 CROSSREFS Column 9 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, this sequence. Sequence in context: A309791 A103935 A040077 * A248311 A302536 A038293 Adjacent sequences:  A195309 A195310 A195311 * A195313 A195314 A195315 KEYWORD nonn,easy,mult AUTHOR Omar E. Pol, Sep 14 2011 STATUS approved

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Last modified October 14 18:28 EDT 2019. Contains 328022 sequences. (Running on oeis4.)