OFFSET
0,3
COMMENTS
Partial sums give the generalized 28-gonal numbers (A303812).
a(n) is also the length of the n-th line segment of the rectangular spiral whose vertices are the generalized 28-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) = 24*n, a(2n+1) = 2*n + 1.
G.f.: x*(1 + 24*x + x^2)/((1-x)^2*(1+x)^2). - Vincenzo Librandi, Jul 28 2018
a(n) = 2*a(n-2) - a(n-4) for n>3. - Colin Barker, Jul 29 2018
Multiplicative with a(2^e) = 3*2^(e+2), and a(p^e) = p^e for an odd prime p. - Amiram Eldar, Oct 14 2023
Dirichlet g.f.: zeta(s-1) * (1 + 11*2^(1-s)). - Amiram Eldar, Oct 26 2023
MATHEMATICA
Table[If[EvenQ[n], 24 (n/2), n], {n, 0, 70}] (* Vincenzo Librandi, Jul 28 2018 *)
With[{nn=40}, Riffle[24*Range[0, nn], 2*Range[0, nn]+1]] (* or *) LinearRecurrence[ {0, 2, 0, -1}, {0, 1, 24, 3}, 80] (* Harvey P. Dale, Jul 06 2019 *)
PROG
(Magma) &cat[[24*n, 2*n + 1]: n in [0..30]]; // Vincenzo Librandi, Jul 28 2018
(PARI) concat(0, Vec(x*(1 + 24*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