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A110048 Expansion of 1/((2*x+1)*(1-4*x-4*x^2)). 3
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; text; internal format)
OFFSET

0,2

COMMENTS

See also comment for A110047.

LINKS

Table of n, a(n) for n=0..21.

Robert Munafo, Sequences Related to Floretions

Index entries for linear recurrences with constant coefficients, signature (2, 12, 8).

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

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'

MATHEMATICA

CoefficientList[Series[1/((2x+1)(1-4x-4x^2)), {x, 0, 30}], x] (* or *) LinearRecurrence[ {2, 12, 8}, {1, 2, 16}, 30] (* Harvey P. Dale, Nov 02 2011 *)

CROSSREFS

Cf. A084159, A086346, A079291, A110046, A110047, A110049, A110050, A086348.

Sequence in context: A127276 A076616 A222381 * A094505 A035598 A167566

Adjacent sequences:  A110045 A110046 A110047 * A110049 A110050 A110051

KEYWORD

easy,nonn

AUTHOR

Creighton Dement, Jul 10 2005

STATUS

approved

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Last modified March 25 19:24 EDT 2017. Contains 284082 sequences.