

A195140


Multiples of 5 and odd numbers interleaved.


23



0, 1, 5, 3, 10, 5, 15, 7, 20, 9, 25, 11, 30, 13, 35, 15, 40, 17, 45, 19, 50, 21, 55, 23, 60, 25, 65, 27, 70, 29, 75, 31, 80, 33, 85, 35, 90, 37, 95, 39, 100, 41, 105, 43, 110, 45, 115, 47, 120, 49, 125, 51, 130, 53, 135, 55, 140, 57, 145, 59, 150, 61, 155, 63
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


COMMENTS

This is 5*n/2 if n is even, n if n is odd.
Partial sums give the generalized enneagonal numbers A118277.
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 enneagonal 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(2n) = 5n, a(2n+1) = 2n+1.
G.f.: x*(1+5*x+x^2) / ((x1)^2*(x+1)^2).  Alois P. Heinz, Sep 26 2011
From Bruno Berselli, Sep 27 2011: (Start)
a(n) = (7+3*(1)^n)*n/4.
a(n) = a(n) = a(n2)*n/(n2) = 2*a(n2)a(n4).
a(n) + a(n1) = A047336(n). (End)
Multiplicative with a(2^e) = 5*2^(e1), a(p^e) = p^e for odd prime p.  Andrew Howroyd, Jul 23 2018


MATHEMATICA

With[{nn=40}, Riffle[5*Range[0, nn], Range[1, 2nn+1, 2]]] (* or *) LinearRecurrence[ {0, 2, 0, 1}, {0, 1, 5, 3}, 80] (* Harvey P. Dale, Dec 15 2014 *)


PROG

(MAGMA) &cat[[5*n, 2*n+1]: n in [0..31]]; // Bruno Berselli, Sep 27 2011
(PARI) a(n)=(7+3*(1)^n)*n/4 \\ Charles R Greathouse IV, Oct 07 2015


CROSSREFS

A008587 and A005408 interleaved.
Column 5 of A195151.
Cf. Sequences whose partial sums give the generalized ngonal numbers, if n>=5: A026741, A001477, zero together with A080512, A022998, this sequence, zero together with A165998, A195159, A195161, A195312.
Sequence in context: A221715 A248660 A141620 * A049829 A258333 A137613
Adjacent sequences: A195137 A195138 A195139 * A195141 A195142 A195143


KEYWORD

nonn,easy,mult


AUTHOR

Omar E. Pol, Sep 10 2011


EXTENSIONS

Corrected and edited by Alois P. Heinz, Sep 25 2011


STATUS

approved



