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Search: id:A109437
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| A109437 |
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a(n) = 5a(n-1) - 5a(n-2) + a(n-3) + 2*(-1)^(n+1), alternatively a(n) = 3a(n-1) + 3a(n-2) - a(n-3). |
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2
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| 0, 1, 3, 12, 44, 165, 615, 2296, 8568, 31977, 119339, 445380, 1662180, 6203341, 23151183, 86401392, 322454384, 1203416145, 4491210195, 16761424636, 62554488348, 233456528757, 871271626679, 3251629977960, 12135248285160
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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See A105968 for a similar sequence. Observe the four periodic sequences (1,1,1,1,); (-1,-1,-1,-1); (1,-1,1,-1,); (-1,1,-1,1,); (a(n)) is the (Type 1A) jbasejfor-transform of the periodic sequence (1,1,1,1) with respect to the floretion given in the program code. A109438 is the (Type 1A) jbasejfor-transform of the periodic sequence (-1,-1,-1,-1) with respect to the floretion given in the program code. A001834 is the (Type 1A) jbasejfor-transform of the periodic sequence (1,-1,1,-1) with respect to the floretion given in the program code. A102871 is the (Type 1A) jbasejfor-transform of the periodic sequence (-1,1,-1,1) with respect to the floretion given in the program code.
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FORMULA
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G.f. x/((x+1)(x^2-4x+1))
Equals A002530(n)*A002530(n+1). - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 08 2007
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MAPLE
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with(numtheory):a := cfrac (tan(Pi/3), 60): > b := cfrac (tan(Pi/6), 60): > seq(nthnumer (b, i)*nthdenom (a, i), i=0..24 ); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Feb 08 2007
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PROGRAM
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Floretion Algebra Multiplication Program, FAMP Code: (-1)^(n+1)jbasejfor[ + .5'ii' + .5'kk' + .5'ij' + .5'ji' + .5'jk' + .5'kj'] 1vesfor = (1, 1, 1, 1, )
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CROSSREFS
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Cf. A109438, A001834, A102871.
Cf. A002530.
Sequence in context: A066987 A012873 A167477 this_sequence A005656 A064017 A005320
Adjacent sequences: A109434 A109435 A109436 this_sequence A109438 A109439 A109440
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KEYWORD
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nonn
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AUTHOR
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Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Jun 28 2005
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