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Search: id:A122552
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| A122552 |
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a(0)=a(1)=a(2)=1, a(n)=a(n-1)+a(n-2)+2*a(n-3) for n>2. |
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+0
3
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| 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)
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OFFSET
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0,4
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COMMENT
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Equals INVERT transform of (1, 0, 3, 0, 3, 0, 3,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Apr 27 2009]
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FORMULA
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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]
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PROGRAM
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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
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CROSSREFS
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Sequence in context: A074864 A074865 A072683 this_sequence A074862 A101064 A055675
Adjacent sequences: A122549 A122550 A122551 this_sequence A122553 A122554 A122555
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KEYWORD
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nonn
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 20 2006
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EXTENSIONS
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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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