OFFSET
0,2
COMMENTS
Interpolated zeros suppressed.
The inverse mod 2 binomial transform of 2^n is 1,1,3,3,15,15,... (A100735).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (0,15).
FORMULA
a(n) = b(2*n) where b(0)=1, b(1)=0, b(n) = (5 - 2*(n/2 mod 2))b(n-2).
a(n) = A101553(2*(n+1))/5.
a(2*n) = 15^n, a(2*n+1) = 3 * 15^n. - Ralf Stephan, May 16 2007
O.g.f.: (1+3*x)/(1-15*x^2). - R. J. Mathar, Feb 04 2008
From Amiram Eldar, Feb 04 2026: (Start)
E.g.f.: cosh(sqrt(15)*x) + sqrt(3/5)*sinh(sqrt(15)*x).
Sum_{n>=0} 1/a(n) = 10/7.
Sum_{n>=0} (-1)^n/a(n) = 5/7. (End)
MAPLE
a:=n->mul(4+(-1)^j, j=1..n):seq(a(n), n=0..23); # Zerinvary Lajos, Dec 13 2008
MATHEMATICA
LinearRecurrence[{0, 15}, {1, 3}, 50] (* G. C. Greubel, Apr 16 2018 *)
(* Alternative: *)
RecurrenceTable[{a[n] == (5 - 2*Mod[n/2, 2])*a[n - 2], a[0] == 1, a[1] == 0}, a, {n, 0, 50}][[1 ;; ;; 2]] (* G. C. Greubel, Apr 16 2018 *)
PROG
(PARI) my(x='x+O('x^30)); Vec((1+3*x)/(1-15*x^2)) \\ G. C. Greubel, Apr 16 2018
(Magma) I:=[1, 3]; [n le 2 select I[n] else 15*Self(n-2): n in [1..30]]; // G. C. Greubel, Apr 16 2018
CROSSREFS
KEYWORD
easy,nonn,changed
AUTHOR
Paul Barry, Dec 06 2004
STATUS
approved