

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

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



FORMULA

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
Dirichlet g.f.: zeta(s1) * (1 + 2^(3s)).  Amiram Eldar, Oct 25 2023


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



CROSSREFS

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.


KEYWORD

nonn,easy,mult


AUTHOR



STATUS

approved



