A096886 - OEIS

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A096886

Expansion of (1+3x)/(1-8x^2).

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; internal format)

	OFFSET	`0,2`
	COMMENTS	`Contribution from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 12 2010: (Start)` `Apparently the row n=3 of an array T(n,k) counting walks with k steps on a n-by-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)`
	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 (pbarry(AT)wit.ie), Jul 14 2004`

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Last modified February 16 21:51 EST 2012. Contains 205978 sequences.