

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
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OFFSET

0,3


COMMENTS

A008592 and A005408 interleaved.
Partial sums give the generalized 14gonal (or tetradecagonal) numbers A195818.
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 14gonal 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))/((1x)^2*(1+x)^2).
a(n) = a(n) = a(n2)*n/(n2) = 2*a(n2)a(n4).
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(n2)a(n4).  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 ngonal 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: A064211 A050133 A068608 * A228314 A243239 A079670
Adjacent sequences: A195814 A195815 A195816 * A195818 A195819 A195820


KEYWORD

nonn,easy,mult


AUTHOR

Omar E. Pol, Sep 29 2011


STATUS

approved



