OFFSET
0,3
COMMENTS
Partial sums give the generalized 14-gonal (or tetradecagonal) numbers A195818.
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 14-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(n) = (2*(-1)^n+3)*n. - Vincenzo Librandi, Sep 30 2011
From Bruno Berselli, Sep 30 2011: (Start)
G.f.: x*(1+10*x+x^2)/((1-x)^2*(1+x)^2).
a(n) = -a(-n) = a(n-2)*n/(n-2) = 2*a(n-2)-a(n-4).
a(n) * a(n+1) = a(n(n+1)).
a(n) + a(n+1) = A091998(n+1). (End)
a(0)=0, a(1)=1, a(2)=10, a(3)=3, a(n)=2*a(n-2)-a(n-4). - Harvey P. Dale, Nov 24 2013
Multiplicative with a(2^e) = 5*2^e, a(p^e) = p^e for odd prime p. - Andrew Howroyd, Jul 23 2018
Dirichlet g.f.: zeta(s-1) * (1 + 2^(3-s)). - Amiram Eldar, Oct 25 2023
MATHEMATICA
With[{nn=30}, Riffle[10*Range[0, nn], Range[1, 2*nn+1, 2]]] (* or *) LinearRecurrence[{0, 2, 0, -1}, {0, 1, 10, 3}, 70] (* Harvey P. Dale, Nov 24 2013 *)
PROG
(Magma) [(2*(-1)^n+3)*n: n in [0..60]]; // Vincenzo Librandi, Sep 30 2011
(PARI) a(n) = (2*(-1)^n+3)*n; \\ Andrew Howroyd, Jul 23 2018
CROSSREFS
KEYWORD
nonn,easy,mult,changed
AUTHOR
Omar E. Pol, Sep 29 2011
STATUS
approved