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
Examples
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
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).
Programs
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GAP
List([0..35],n->n*2^(n-2)*(9+(-1)^n)); # Muniru A Asiru, Jul 10 2018
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Magma
/* By definition: */ [Integers()!(n*4^(n/2-1)*(9+(-1)^n)): n in [0..40]]; // Bruno Berselli, Mar 29 2016
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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
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Maple
See A187272.
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Mathematica
LinearRecurrence[{0,8,0,-16},{0,4,20,48},40] (* Harvey P. Dale, Dec 25 2014 *) -
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<
Chai Wah Wu, Feb 18 2024
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