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Search: id:A001648
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| A001648 |
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Tetranacci numbers A073817 without the leading term 4.
(Formerly M2648 N1055)
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+0
9
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| 1, 3, 7, 15, 26, 51, 99, 191, 367, 708, 1365, 2631, 5071, 9775, 18842, 36319, 70007, 134943, 260111, 501380, 966441, 1862875, 3590807, 6921503, 13341626, 25716811, 49570747, 95550687, 184179871, 355018116, 684319421, 1319068095, 2542585503
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Fielder, Daniel C.; Special integer sequences controlled by three parameters. Fibonacci Quart 6 1968 64-70.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..200
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Eric Weisstein's World of Mathematics, Lucas n-Step Number
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FORMULA
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G.f.: x(1+2*x+3*x^2+4*x^3)/(1-x-x^2-x^3-x^4).
a(n) = trace of M^n, where M = the 4 X 4 matrix [ 0 1 0 0 / 0 0 1 0 / 0 0 0 1 / 1 1 1 1]. E.g. the trace (sum of diagonal terms) of M^12 = a(12) = 2631 = (108 + 316 + 717 + 1490). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Feb 22 2004
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MAPLE
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A001648:=-(1+2*z+3*z**2+4*z**3)/(-1+z+z**2+z**3+z**4); [Conjectured by S. Plouffe in his 1992 dissertation.]
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PROGRAM
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(PARI) a(n)=if(n<0, 0, polcoeff(x*(1+2*x+3*x^2+4*x^3)/(1-x-x^2-x^3-x^4)+x*O(x^n), n))
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CROSSREFS
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Cf. A000288, A073817.
Sequence in context: A078869 A011890 A131076 this_sequence A051054 A001649 A001276
Adjacent sequences: A001645 A001646 A001647 this_sequence A001649 A001650 A001651
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KEYWORD
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nonn,easy
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AUTHOR
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njas
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