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A096886 Expansion of (1+3x)/(1-8x^2). 4
1, 3, 8, 24, 64, 192, 512, 1536, 4096, 12288, 32768, 98304, 262144, 786432, 2097152, 6291456, 16777216, 50331648, 134217728, 402653184, 1073741824, 3221225472, 8589934592, 25769803776, 68719476736, 206158430208, 549755813888 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

From R. J. Mathar, Oct 12 2010: (Start)

Apparently the row n=3 of an array T(n,k) counting walks with k steps on a n X n board starting at an edge position next to a corner, each step to one of the <=4 adjacent squares:

1,3,8,24,64,192,512,1536,4096,12288,32768,98304,262144,

1,3,9,29,93,301,973,3149,10189,32973,106701,345293,1117389,

1,3,9,30,99,342,1161,4050,13851,48438,165969,580770,1990899,

1,3,9,30,100,349,1216,4329,15381,55187,197714,711458,2557699,

1,3,9,30,100,350,1224,4400,15776,57552,209088,768768,2812160,

1,3,9,30,100,350,1225,4409,15865,58091,212586,786708,2909166,

1,3,9,30,100,350,1225,4410,15875,58200,213300,791700,2936375,

1,3,9,30,100,350,1225,4410,15876,58211,213431,792623,2943291,

1,3,9,30,100,350,1225,4410,15876,58212,213443,792778,2944460,

1,3,9,30,100,350,1225,4410,15876,58212,213444,792791,2944641, (End)

LINKS

Table of n, a(n) for n=0..26.

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

FORMULA

a(n) = (1 + (-1)^n)8^floor((n+1)/2)/2 + 3(1-(-1)^n)8^floor(n/2)/2;

a(n) = 2^(3n/2)(3sqrt(2)/8+1/2 - (3sqrt(2)/8-1/2)(-1)^n).

a(2n+1) = 2a(2n) + 2a(2n-1) + 2a(2n-2);

a(2n) = 2a(2n-1) + 2a(2n-2).

a(n+3) = a(n+2)*a(n+1)/a(n). [Reinhard Zumkeller, Mar 04 2011]

CROSSREFS

Cf. A038754.

Sequence in context: A026556 A096001 A080097 * A176904 A056332 A091588

Adjacent sequences:  A096883 A096884 A096885 * A096887 A096888 A096889

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jul 14 2004

STATUS

approved

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Last modified May 27 15:22 EDT 2017. Contains 287207 sequences.