

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
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OFFSET

0,3


COMMENTS

Partial sums give the generalized 13gonal (or tridecagonal) numbers A195313.
a(n) is also the length of the nth line segment of a rectangular spiral on the infinite square grid. The vertices of the spiral are the generalized 13gonal 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)/((1x)^2*(1+x)^2).
a(n) = (7*(1)^n+11)*n/4.
a(n) + a(n1) = A175885(n).
Sum_{i=0..n} a(i) = A195313(n). (End)
Multiplicative with a(2^e) = 9*2^(e1), 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 ngonal 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



