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A110526
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a(n+3) = 3*a(n+2) + 5*a(n+1) + a(n), a(0) = 0, a(1) = 1, a(2) = 3.
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4
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0, 1, 3, 14, 58, 247, 1045, 4428, 18756, 79453, 336567, 1425722, 6039454, 25583539, 108373609, 459077976, 1944685512, 8237820025, 34895965611, 147821682470, 626182695490, 2652552464431, 11236392553213, 47598122677284
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OFFSET
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0,3
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COMMENTS
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A001076(n) = a(n) + a(n+1). Program "Superseeker" finds: A033887(n+1) = a(n+2) - a(n); Elements of even index in the sequence: A049661(n) = (F(6n+1)-1)/4; A015448(n+2) = a(n+2) + 2*a(n+1) + a(n)
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LINKS
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Table of n, a(n) for n=0..23.
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FORMULA
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G.f. -x/((1+x)*(x^2+4*x-1)
a(n)=(1/8)*[2-sqrt(5)]^n-(1/4)*(-1)^n+(1/8)*[2+sqrt(5)]^n+(1/40)*[2+sqrt(5)]^n*sqrt(5)-(1/40) *[2-sqrt(5)]^n*sqrt(5), with n>=0 [From Paolo P. Lava, Oct 02 2008]
a(n) = (-1)^n/2 * sum(k=0..n, (-1)^k*Fibonacci(3*k)). [Gary Detlefs, Jan 03 2013]
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MAPLE
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seriestolist(series(-x/((1+x)*(x^2+4*x-1)), x=0, 25)); -or- Floretion Algebra Multiplication Program, FAMP Code: 1jbaseseq[(- 'i + 'j - i' + j' - 'kk' - 'ik' - 'jk' - 'ki' - 'kj')(+ .5'i + .5i' + .5'jj' + .5'kk')]
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CROSSREFS
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Cf. A110526, A110527, A033887, A001076, A049661, A033887.
Sequence in context: A127363 A133444 A126875 * A038679 A151235 A151236
Adjacent sequences: A110523 A110524 A110525 * A110527 A110528 A110529
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KEYWORD
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easy,nonn
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AUTHOR
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Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Jul 24 2005
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STATUS
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approved
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