A159582 Expansion of (1+6*x+x^2-2*x^3)/((x^2+2*x-1)*(x^2-2*x-1)), bisection is NSW numbers.

1, 6, 7, 34, 41, 198, 239, 1154, 1393, 6726, 8119, 39202, 47321, 228486, 275807, 1331714, 1607521, 7761798, 9369319, 45239074, 54608393, 263672646, 318281039, 1536796802, 1855077841, 8957108166, 10812186007, 52205852194, 63018038201, 304278004998

Offset

0,2

Comments

Define c = [0, 7, 0, 41, 0, 239, 0, 1393, 0, 8119, 0, 47321, ...] where (c(2n+1)) = A002315(n+1) (NSW numbers). Then (a(n)) has the property c(2n) - a(2n) = -a(2n) = -A002315(n) and c(2n+1) - a(2n+1) = A002315(n) (NSW numbers).

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (0,6,0,-1).

Formula

a(n) = 3*A078057(n)/2 - (-1)^n*A078057(n)/2. - R. J. Mathar, Nov 10 2009

From Colin Barker, Jun 29 2017: (Start)

a(n) = 6*a(n-2) - a(n-4) for n>3.

a(n) = ((-(-2+sqrt(2))*(-1+sqrt(2))^n - (-1-sqrt(2))^n*(2+sqrt(2)) - 3*(-(1-sqrt(2))^n*(-2+sqrt(2)) - (1+sqrt(2))^n*(2+sqrt(2))))) / (4*sqrt(2)).

(End)

Prog

(PARI) Vec((1+6*x+x^2-2*x^3) / ((x^2+2*x-1)*(x^2-2*x-1)) + O(x^50)) \\ Colin Barker, Jun 29 2017

Crossrefs

Cf. A002315.

Sequence in context: A348950 A292106 A037375 * A041553 A047190 A359530

Adjacent sequences: A159579 A159580 A159581 * A159583 A159584 A159585

Keyword

easy,nonn

Author

Creighton Dement, Apr 16 2009

Status

approved