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A094015
Expansion of (1+4*x)/(1-8*x^2).
8
1, 4, 8, 32, 64, 256, 512, 2048, 4096, 16384, 32768, 131072, 262144, 1048576, 2097152, 8388608, 16777216, 67108864, 134217728, 536870912, 1073741824, 4294967296, 8589934592, 34359738368, 68719476736, 274877906944
OFFSET
0,2
COMMENTS
Row sums of triangle A135838. - Gary W. Adamson, Dec 01 2007
Row sums of triangle A152842. - Reinhard Zumkeller, May 01 2014
FORMULA
a(n) = 2^(3*n/2)*(1 + sqrt(2) + (-1)^n*(1 - sqrt(2)))/2.
a(n) = (1/4)*(3 + (-1)^n)*8^floor((n+1)/2). - Paul Barry, Jul 14 2004
a(n) = (1 + sqrt(2))*(2*sqrt(2))^n/2 + (1 - sqrt(2))*(-2*sqrt(2))^n/2. Third binomial transform is A002315 (NSW numbers). - Paul Barry, Jul 17 2004
a(n) = 2^A007494(n). - Paul Barry, Aug 18 2007
a(n) = A016116(n+1)*A000079(n). - R. J. Mathar, Jul 08 2009
a(n+3) = a(n+2)*a(n+1)/a(n). - Reinhard Zumkeller, Mar 04 2011
a(n) = 8^floor(n/2)*A010685(n). - G. C. Greubel, Nov 22 2021
MAPLE
a:=n->mul(3-(-1)^j, j=1..n):seq(a(n), n=0..25); # Zerinvary Lajos, Dec 13 2008
MATHEMATICA
Table[8^Floor[n/2]*Mod[4^n, 5], {n, 0, 30}] (* G. C. Greubel, Nov 22 2021 *)
PROG
(Haskell)
a094015 = sum . a152842_row -- Reinhard Zumkeller, May 01 2014
(Magma) [2*8^Floor((n-1)/2)*(3+(-1)^n): n in [0..30]]; // G. C. Greubel, Nov 22 2021
(Sage) [8^(n//2)*(4^n%5) for n in (0..30)] # G. C. Greubel, Nov 22 2021
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Apr 21 2004
STATUS
approved