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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
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 (list; graph; refs; listen; history; text; internal format)
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: A095369 A006493 A037375 * A041553 A047190 A237711

Adjacent sequences:  A159579 A159580 A159581 * A159583 A159584 A159585

KEYWORD

easy,nonn

AUTHOR

Creighton Dement, Apr 16 2009

STATUS

approved

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Last modified August 18 12:24 EDT 2017. Contains 290720 sequences.