The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A184418 Convolution square of A040001. 2
1, 2, 5, 6, 10, 10, 15, 14, 20, 18, 25, 22, 30, 26, 35, 30, 40, 34, 45, 38, 50, 42, 55, 46, 60, 50, 65, 54, 70, 58, 75, 62, 80, 66, 85, 70, 90, 74, 95, 78, 100, 82, 105, 86, 110, 90, 115, 94, 120, 98, 125, 102, 130, 106, 135, 110, 140, 114, 145, 118, 150, 122, 155, 126 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
G.f.: (1 + x + x^2)^2 / (1 - x^2)^2 = 1 + x * (x + 2) * (2*x + 1) / (1 - x^2)^2. a(-n) = -a(n) except a(0) = 2.
Euler transform of length 3 sequence [2, 2, -2].
a(n) = 2 * b(n) where b() is multiplicative with b(2^e) = 5 * 2^(e-2) if e>0, b(p^e) = p^e if p>2.
a(2*n + 1) = 4*n + 2, a(2*n) = 5*n except a(0) = 2.
a(n) = (9+(-1)^n)*n/4 = (n/2)*A010710(n+1) for n>0. - Bruno Berselli, Mar 24 2011
EXAMPLE
G.f. = 1 + 2*x + 5*x^2 + 6*x^3 + 10*x^4 + 10*x^5 + 15*x^6 + 14*x^7 + 20*x^8 + ...
MATHEMATICA
LinearRecurrence[{0, 2, 0, -1}, {1, 2, 5, 6, 10}, 80] (* Harvey P. Dale, Jul 03 2017 *)
PROG
(PARI) {a(n) = (n==0) + n * ([5/2, 2] [n%2 + 1])};
(PARI) {a(n) = if( n==0, 1, sign(n) * polcoeff( (1 + x + x^2)^2 / (1 - x^2)^2 + x * O(x^abs(n)), abs(n)))};
(Magma) I:=[2, 5, 6, 10]; [1] cat [n le 4 select I[n] else 2*Self(n-2) - Self(n-4): n in [1..30]]; // G. C. Greubel, Aug 14 2018
CROSSREFS
Sequence in context: A295741 A007503 A337298 * A112967 A244731 A307562
KEYWORD
nonn
AUTHOR
Michael Somos, Feb 14 2011
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 00:34 EDT 2024. Contains 372608 sequences. (Running on oeis4.)