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A110048
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Expansion of 1/((2*x+1)*(1-4*x-4*x^2)).
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3
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1, 2, 16, 64, 336, 1568, 7680, 36864, 178432, 860672, 4157440, 20070400, 96915456, 467935232, 2259419136, 10909384704, 52675280896, 254338531328, 1228055511040, 5929575645184, 28630525673472, 138240403177472
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| See also comment for A110047.
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LINKS
| Robert Munafo, Sequences Related to Floretions
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FORMULA
| Superseeker finds: a(n+1) = 2*A086348(n+1) (A086348's offset is 1: On a 3 X 3 board, number of n-move routes of chess king ending at central cell); binomial transform matches A084159 (Pell oblongs); j-th coefficient of g.f.*(1+x)^j matches A079291 (Squares of Pell numbers); a(n) + a(n+1) = A086346(n+2) (A086346's offset is 1: On a 3 X 3 board, the number of n-move paths for a chess king ending in a given corner cell.)
Recurrence: a(n)=2*a(n-1)+12*a(n-2)+8*a(n-3), where a(1)=1, a(2)=2, a(3)=16; formula a(n)=(1/4)*(-1)^(1-n)*2^n+(1/8)*2^n*(sqrt(2)-1)^(-n)+(1/8)*2^n*(-sqrt(2)-1)^(-n). - Maksym Voznyy (voznyy(AT)mail.ru), Jul 24 2008
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MAPLE
| seriestolist(series(-1/((2*x+1)*(4*x^2+4*x-1)), x=0, 25)); -or- Floretion Algebra Multiplication Program, FAMP Code: -kbasejseq[A*B] with A = + 'i - .5'j + .5'k - .5j' + .5k' - 'ii' - .5'ij' - .5'ik' - .5'ji' - .5'ki' and B = - .5'i + .5'j + 'k - .5i' + .5j' - 'kk' - .5'ik' - .5'jk' - .5'ki' - .5'kj'
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MATHEMATICA
| CoefficientList[Series[1/((2x+1)(1-4x-4x^2)), {x, 0, 30}], x] (* or *) LinearRecurrence[ {2, 12, 8}, {1, 2, 16}, 30] (* From Harvey P. Dale, Nov 02 2011 *)
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CROSSREFS
| Cf. A084159, A086346, A079291, A110046, A110047, A110049, A110050, A086348.
Sequence in context: A061608 A127276 A076616 * A094505 A035598 A167566
Adjacent sequences: A110045 A110046 A110047 * A110049 A110050 A110051
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KEYWORD
| easy,nonn
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AUTHOR
| Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Jul 10 2005
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