A195159 Multiples of 7 and odd numbers interleaved.

0, 1, 7, 3, 14, 5, 21, 7, 28, 9, 35, 11, 42, 13, 49, 15, 56, 17, 63, 19, 70, 21, 77, 23, 84, 25, 91, 27, 98, 29, 105, 31, 112, 33, 119, 35, 126, 37, 133, 39, 140, 41, 147, 43, 154, 45, 161, 47, 168, 49, 175, 51, 182, 53, 189, 55, 196, 57, 203, 59, 210, 61

Offset: 0

Author

Omar E. Pol, Sep 10 2011

Keywords

• nonn
• easy
• mult

Comments

This is 7*n if n is even, n if n is odd, if n>=0.

Partial sums give the generalized 11-gonal (or hendecagonal) numbers A195160.

a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 11-gonal 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

Cf. A008589 and A005408 interleaved.

Column k=7 of A195151.

Cf. Sequences whose partial sums give the generalized n-gonal numbers, if n>=5: A026741, A001477, zero together with A080512, A022998, A195140, zero together with A165998, this sequence, A195161.

Cf. A056020, A195160.

Programs

Magma

&cat[[7*n, 2*n+1]: n in [0..40]]; // Vincenzo Librandi, Sep 27 2011

Mathematica

Table[If[EvenQ[n], 7(n/2), n], {n, 0, 61}] (* Alonso del Arte, Sep 14 2011 *)
With[{nn=40},Riffle[7*Range[0,nn],Range[1,2nn,2]]] (* Harvey P. Dale, Aug 01 2019 *)

PARI

a(n)=(5*(-1)^n+9)*n/4 \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(2n) = 7n, a(2n+1) = 2n+1. [corrected by Omar E. Pol, Jul 26 2018]

From Bruno Berselli, Sep 14 2011: (Start)

G.f.: x*(1+7*x+x^2)/((1-x)^2*(1+x)^2).

a(n) = (5*(-1)^n+9)*n/4.

a(n) + a(n-1) = A056020(n). (End)

Multiplicative with a(2^e) = 7*2^(e-1), a(p^e) = p^e for odd prime p. - Andrew Howroyd, Jul 23 2018

Dirichlet g.f.: zeta(s-1) * (1 + 5/2^s). - Amiram Eldar, Oct 25 2023