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A143099 A007318 * A143097. 3
1, 3, 9, 22, 50, 113, 256, 576, 1281, 2818, 6146, 13313, 28672, 61440, 131073, 278530, 589826, 1245185, 2621440, 5505024, 11534337, 24117250, 50331650, 104857601, 218103808, 452984832, 939524097, 1946157058, 4026531842, 8321499137, 17179869184, 35433480192 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

A143100 = (1, 3, 4, 6, 13, 30, 64, 129, ...).

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..1000

FORMULA

Binomial transform of A143097: (1, 2, 4, 3, 5, 7, 6, 8, 10, 9, 11, ...). a(n) = 2*a(n-1) + A143100(n-1).

G.f.: x*(5*x^4-7*x^3+5*x^2-3*x+1)/((1-x)*(x^2-x+1)*(1-2*x)^2). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 14 2009; [corrected by R. J. Mathar, Sep 16 2009]

EXAMPLE

a(4) = 22 = (1, 3, 3, 1) dot (1, 2, 4, 3) = (1 + 6 + 12 + 3).

a(4) = 22 = 2*a(3) + A143099(3) = 2*9 + 4, where 4 = A143100(3).

MAPLE

A143097 := proc(n) if(n<=1)then return n: elif(n mod 3 <= 1)then return n+1-2*(n mod 3): else return n: fi: end: A143099 := proc(n) return add(binomial(n-1, k-1)*A143097(k), k=1..n): end: seq(A143099(n), n=1..32); # Nathaniel Johnston, Apr 30 2011

CROSSREFS

Cf. A143097, A143098, A143100.

Sequence in context: A000715 A260545 A034505 * A160462 A000711 A278668

Adjacent sequences:  A143096 A143097 A143098 * A143100 A143101 A143102

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Jul 24 2008

STATUS

approved

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Last modified June 1 02:09 EDT 2020. Contains 334758 sequences. (Running on oeis4.)