A104721 Expansion of (1+x)^2/(1-4*x^2).

1, 2, 5, 8, 20, 32, 80, 128, 320, 512, 1280, 2048, 5120, 8192, 20480, 32768, 81920, 131072, 327680, 524288, 1310720, 2097152, 5242880, 8388608, 20971520, 33554432, 83886080, 134217728, 335544320, 536870912, 1342177280, 2147483648

Offset

0,2

Comments

Binomial transform is A033113.

Let b(n) = binomial(n-1, (n-1)/2)*(1-(-1)^n)/2 + binomial(n, n/2)*(1+(-1)^n)/2. Then a(n) = Sum_{k=0..n} b(k)*b(n-k).

If a(1)=2 is dropped, sequence becomes identical to A084568 (Proof immediate by standard manipulation of the two generating functions). - R. J. Mathar, May 19 2008

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,4).

Formula

a(n) = (9*2^n + (-2)^n - 2*0^n)/8.

Mathematica

CoefficientList[Series[(1+x)^2/(1-4x^2), {x, 0, 40}], x] (* or *) LinearRecurrence[{0, 4}, {1, 2, 5}, 40] (* Harvey P. Dale, Dec 05 2015 *)

Prog

(PARI) vector(40, n, n--; (9*2^n +(-2)^n -2*0^n)/8) \\ G. C. Greubel, Jul 14 2019
(Magma) [1] cat [9*2^(n-3) -(-2)^(n-3): n in [1..40]]; // G. C. Greubel, Jul 14 2019
(Sage) [1]+[9*2^(n-3) -(-2)^(n-3) for n in (1..40)] # G. C. Greubel, Jul 14 2019
(GAP) Concatenation([1], List([1..40], n-> 9*2^(n-3) -(-2)^(n-3))); # G. C. Greubel, Jul 14 2019

Crossrefs

Sequence in context: A127281 A054774 A360771 * A245191 A281104 A139407

Adjacent sequences: A104718 A104719 A104720 * A104722 A104723 A104724

Keyword

easy,nonn

Author

Paul Barry, Mar 20 2005

Status

approved