A187274 a(n) = n*4^(n/2 - 1)*(9 + (-1)^n).

0, 4, 20, 48, 160, 320, 960, 1792, 5120, 9216, 25600, 45056, 122880, 212992, 573440, 983040, 2621440, 4456448, 11796480, 19922944, 52428800, 88080384, 230686720, 385875968, 1006632960, 1677721600, 4362076160, 7247757312, 18790481920, 31138512896, 80530636800, 133143986176, 343597383680

Offset

0,2

Links

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

R. Kemp, On the number of words in the language {w in Sigma* | w = w^R }^2, Discrete Math., 40 (1982), 225-234. See Lemma 1.

Index entries for linear recurrences with constant coefficients, signature (0,8,0,-16).

Formula

a(n) = 8*a(n-2) - 16*a(n-4). - Colin Barker, Jul 25 2013

G.f.: 4*x*(x+1)*(4*x+1) / ((2*x-1)^2*(2*x+1)^2). - Colin Barker, Jul 25 2013

a(2*n) = 5*n*4^n, a(2*n+1) = (2*n+1)*4^(n+1). - Andrew Howroyd, Mar 28 2016

a(n) = -(4^n) * a(-n) for all n in Z. - Michael Somos, Jul 10 2018

Example

G.f. = 4*x + 20*x^2 + 48*x^3 + 160*x^4 + 320*x^5 + 960*x^6 + 1792*x^7 + ... - Michael Somos, Jul 10 2018

Maple

See A187272.

Mathematica

LinearRecurrence[{0, 8, 0, -16}, {0, 4, 20, 48}, 40] (* Harvey P. Dale, Dec 25 2014 *)

Prog

(Magma) /* By definition: */ [Integers()!(n*4^(n/2-1)*(9+(-1)^n)): n in [0..40]]; // Bruno Berselli, Mar 29 2016
(Magma) I:=[0, 4, 20, 48]; [n le 4 select I[n] else 8*Self(n-2)-16*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Mar 29 2016
(GAP) List([0..35], n->n*2^(n-2)*(9+(-1)^n)); # Muniru A Asiru, Jul 10 2018
(PARI) x='x+O('x^50); concat([0], Vec(4*x*(x+1)*(4*x+1)/((2*x-1)^2*(2*x+ 1)^2))) \\ G. C. Greubel, Aug 14 2018
(Python)
def A187274(n): return n<<n+1 if n&1 else 5*(n>>1)<<n # Chai Wah Wu, Feb 18 2024

Crossrefs

Sequence in context: A033579 A294630 A160799 * A367915 A368112 A108099

Adjacent sequences: A187271 A187272 A187273 * A187275 A187276 A187277

Keyword

nonn,easy

Author

N. J. A. Sloane, Mar 07 2011

Status

approved