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A141025 (2^(2+n)-(-1)^n)/3-2*n. 1
1, 1, 1, 5, 13, 33, 73, 157, 325, 665, 1345, 2709, 5437, 10897, 21817, 43661, 87349, 174729, 349489, 699013, 1398061, 2796161, 5592361, 11184765, 22369573, 44739193, 89478433, 178956917, 357913885, 715827825, 1431655705, 2863311469, 5726622997, 11453246057, 22906492177 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,2)

FORMULA

a(n)=3a(n-1)-a(n-2)-3a(n-3)+2a(n-4).

a(n) = A001045(n+2)-2n.

a(n+1)-a(n) = 4*A000975(n-1).

a(n+1)-2a(n)= 2*(n-1)+(-1)^n = -1, -1, 3, 3, 7, 7, 11, 11,... duplicated A004767.

G.f. ( -1+2*x+x^2-6*x^3 ) / ( (1+x)*(2*x-1)*(x-1)^2 ). - R. J. Mathar, Jul 07 2011

PROG

(MAGMA) [(2^(2+n)-(-1)^n)/3-2*n: n in [0..40]]; // Vincenzo Librandi, Aug 08 2011

CROSSREFS

Sequence in context: A272161 A272828 A001981 * A100227 A185454 A278764

Adjacent sequences:  A141022 A141023 A141024 * A141026 A141027 A141028

KEYWORD

nonn,easy

AUTHOR

Paul Curtz, Jul 29 2008

EXTENSIONS

Definition replaced by closed form. - R. J. Mathar, Jul 07 2011

STATUS

approved

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Last modified December 9 06:44 EST 2016. Contains 278963 sequences.