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
KEYWORD
nonn,easy,mult
AUTHOR
Omar E. Pol, Sep 10 2011
STATUS
approved