A094015 Expansion of (1+4*x)/(1-8*x^2).

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

Author

Paul Barry, Apr 21 2004

Keywords

• easy
• nonn

Comments

Row sums of triangle A135838. - Gary W. Adamson, Dec 01 2007

Row sums of triangle A152842. - Reinhard Zumkeller, May 01 2014

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
• Index to divisibility sequences
• Index entries for linear recurrences with constant coefficients, signature (0,8).

Crossrefs

Cf. A010685, A094014, A135838, A152842.

Programs

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

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 *)

Sage

[8^(n//2)*(4^n%5) for n in (0..30)] # G. C. Greubel, Nov 22 2021

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