A110047 Expansion of (1+2*x-4*x^2)/((2*x+1)*(2*x-1)*(4*x^2+4*x-1)).

1, 6, 28, 144, 688, 3360, 16192, 78336, 378112, 1826304, 8817664, 42577920, 205582336, 992649216, 4792926208, 23142334464, 111741042688, 539533639680, 2605098729472, 12578530000896, 60734514921472, 293252181786624, 1415946786832384, 6836795882864640

Offset

0,2

Comments

Note (see program code): ibaseseq[A*B] = A057087, basejseq[A*B] = A099582, tesseq[A*B] = A110046.

Links

Matthew House, Table of n, a(n) for n = 0..1454

Robert Munafo, Sequences Related to Floretions

Index entries for linear recurrences with constant coefficients, signature (4,8,-16,-16).

Formula

a(n) = 4*a(n-1) + 8*a(n-2) - 16*a(n-3) - 16*a(n-4). - Matthew House, Feb 17 2017

a(n) = (-3*(2-2*sqrt(2))^n*(-2+sqrt(2)) + 2^n*(-2*(1+(-1)^n)+3*(1+sqrt(2))^n*(2+sqrt(2)))) / 8. - Colin Barker, Feb 17 2017

Maple

seriestolist(series((1+2*x-4*x^2)/((2*x+1)*(2*x-1)*(4*x^2+4*x-1)), x=0, 25)); -or- Floretion Algebra Multiplication Program, FAMP Code: -kbasekseq[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 + 2 x - 4 x^2)/((2 x + 1)(2 x - 1)(4 x^2 + 4 x - 1)), {x, 0, 21}], x] (* or *)
LinearRecurrence[{4, 8, -16, -16}, {1, 6, 28, 144}, 22] (* Michael De Vlieger, Feb 17 2017 *)

Prog

(PARI) Vec((1+2*x-4*x^2) / ((2*x+1)*(2*x-1)*(4*x^2+4*x-1)) + O(x^30)) \\ Colin Barker, Feb 17 2017

Crossrefs

Cf. A110046, A110048, A110049.

Sequence in context: A053783 A216383 A283094 * A163029 A309490 A344755

Adjacent sequences: A110044 A110045 A110046 * A110048 A110049 A110050

Keyword

easy,nonn

Author

Creighton Dement, Jul 10 2005

Extensions

Definition corrected by Matthew House, Feb 17 2017

Status

approved