A195140 Multiples of 5 and odd numbers interleaved.

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

Offset: 0

Author

Omar E. Pol, Sep 10 2011

Keywords

• nonn
• easy
• mult

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 n-th 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).

Crossrefs

A008587 and A005408 interleaved.

Column 5 of A195151.

Cf. Sequences whose partial sums give the generalized n-gonal numbers, if n>=5: A026741, A001477, zero together with A080512, A022998, this sequence, zero together with A165998, A195159, A195161, A195312.

Cf. A047336, A118277.

Programs

Magma

&cat[[5*n,2*n+1]: n in [0..31]]; // Bruno Berselli, Sep 27 2011

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 *)

PARI

a(n)=(7+3*(-1)^n)*n/4 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(2n) = 5n, a(2n+1) = 2n+1.

G.f.: x*(1+5*x+x^2) / ((x-1)^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(n-2)*n/(n-2) = 2*a(n-2)-a(n-4).

a(n) + a(n-1) = A047336(n). (End)

Multiplicative with a(2^e) = 5*2^(e-1), a(p^e) = p^e for odd prime p. - Andrew Howroyd, Jul 23 2018

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

Extensions

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