OFFSET
0,3
COMMENTS
Partial sums give the generalized 22-gonal numbers (A303299).
a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 22-gonal numbers.
LINKS
Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,2,0,-1).
FORMULA
a(2n) = 18*n, a(2n+1) = 2*n + 1.
From Colin Barker, Jul 29 2018: (Start)
G.f.: x*(1 + 18*x + x^2) / ((1 - x)^2*(1 + x)^2).
a(n) = 2*a(n-2) - a(n-4) for n>3. (End)
Multiplicative with a(2^e) = 9*2^e, and a(p^e) = p^e for an odd prime p. - Amiram Eldar, Oct 14 2023
Dirichlet g.f.: zeta(s-1) * (1 + 2^(4-s)). - Amiram Eldar, Oct 25 2023
MATHEMATICA
a[n_] := If[OddQ[n], n, 9*n]; Array[a, 70, 0] (* Amiram Eldar, Oct 14 2023 *)
PROG
(PARI) concat(0, Vec(x*(1 + 18*x + x^2) / ((1 - x)^2*(1 + x)^2) + O(x^60))) \\ Colin Barker, Jul 29 2018
CROSSREFS
KEYWORD
nonn,easy,mult
AUTHOR
Omar E. Pol, Jul 25 2018
STATUS
approved