OFFSET
0,3
COMMENTS
Partial sums give the generalized 21-gonal numbers (A303298).
a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 21-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) = 17*n, a(2n+1) = 2*n + 1.
From Colin Barker, Jul 29 2018: (Start)
G.f.: x*(1 + 17*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) = 17*2^(e-1), and a(p^e) = p^e for an odd prime p. - Amiram Eldar, Oct 14 2023
Dirichlet g.f.: zeta(s-1) * (1 + 15/2^s). - Amiram Eldar, Oct 25 2023
MATHEMATICA
With[{nn=40}, Riffle[17*Range[0, nn], 2*Range[0, nn]+1]] (* or *) LinearRecurrence[ {0, 2, 0, -1}, {0, 1, 17, 3}, 80] (* Harvey P. Dale, Jun 06 2020 *)
PROG
(PARI) concat(0, Vec(x*(1 + 17*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