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A122552 a(0)=a(1)=a(2)=1, a(n)=a(n-1)+a(n-2)+2*a(n-3) for n>2. +0
3
1, 1, 1, 4, 7, 13, 28, 55, 109, 220, 439, 877, 1756, 3511, 7021, 14044, 28087, 56173, 112348, 224695, 449389, 898780, 1797559, 3595117, 7190236, 14380471, 28760941, 57521884, 115043767, 230087533, 460175068, 920350135, 1840700269, 3681400540 (list; graph; listen)
OFFSET

0,4

COMMENT

Equals INVERT transform of (1, 0, 3, 0, 3, 0, 3,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 27 2009]

FORMULA

a(3*n)=2*a(3*n-1)+2, a(3*n+1)=2*a(3*n)-1, a(3*n+2)=2*a(3*n+1)-1, a(0)=1 . G.f. : (1-x^2)/(1-x-x^2-2*x^3).

a(n)=(3/7)*2^n-(1/7)*I*sqrt(3)*[(-1/2)+(1/2)*I*sqrt(3)]^n+(2/7)*[(-1/2)-(1/2)*I*sqrt(3)]^n+(2 /7)*[(-1/2)+(1/2)*I*sqrt(3)]^n+(1/7)*I*sqrt(3)*[(-1/2)-(1/2)*I*sqrt(3)]^n, with n>=0 and I=sqrt(-1) [From Paolo P. Lava (ppl(AT)spl.at), Nov 19 2008]

a(n)= ( (-1)^n*A130815(n+2)+3*2^n )/7 . [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 30 2008]

A140295(n+2)/4 . a(n+1)-2a(n)=period3:repeat -1,-1,2=-A061347. a(n)-a(n-1)=0,0,3,3,6,15,27,54,111,=3*A077947. a(n)-a(n-2)=0,3,6,9,21,42,81,. a(n)-a(n-3)=3,6,12,24,=A007283=3*A000079. a(3n)+a(3n+1)+a(3n+2)=3,24,192,=A103333(n+1)=A140295(3n)+A140295(3n+1)+A140295(3n+2). See A078010,A139217,A139218. [From Paul Curtz (bpcrtz(AT)free.fr), Oct 02 2009]

PROGRAM

sage: from sage.combinat.sloane_functions import recur_gen3 sage: it = recur_gen3(1, 1, 1, 1, 1, 2) sage: [it.next() for i in range(30)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 25 2008

CROSSREFS

Sequence in context: A074864 A074865 A072683 this_sequence A074862 A101064 A055675

Adjacent sequences: A122549 A122550 A122551 this_sequence A122553 A122554 A122555

KEYWORD

nonn

AUTHOR

Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 20 2006

EXTENSIONS

Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 01 2006, Nov 07 2006

Typo in definition correctred by Paul Curtz, Oct 02 2009

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Last modified November 27 22:38 EST 2009. Contains 167602 sequences.


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