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

0,3

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).

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

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 *)

Prog

(Magma) &cat[[7*n, 2*n+1]: n in [0..40]]; // Vincenzo Librandi, Sep 27 2011
(PARI) a(n)=(5*(-1)^n+9)*n/4 \\ Charles R Greathouse IV, Oct 07 2015

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.

Sequence in context: A061194 A248280 A255772 * A279353 A200943 A357113

Adjacent sequences: A195156 A195157 A195158 * A195160 A195161 A195162

Keyword

nonn,easy,mult

Author

Omar E. Pol, Sep 10 2011

Status

approved