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Search: id:A064551
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| A064551 |
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Ado [Simone Caramel]'s Fibonacci function: define the Fibonacci sequence by f(0) = 1, f(1) = 1, f(n) = f(n-1)+f(n-2); then a(0) = 1, a(n) = a(n-1)+2*(f(n)-n), n > 0. |
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3
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| 1, 1, 1, 1, 3, 9, 23, 51, 103, 195, 353, 619, 1061, 1789, 2981, 4925, 8087, 13221, 21547, 35039, 56891, 92271, 149541, 242231, 392233, 634969, 1027753, 1663321, 2691723, 4355745, 7048223, 11404779, 18453871, 29859579, 48314441, 78175075
(list; graph; listen)
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OFFSET
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0,5
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COMMENT
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A Pickover sequence with properties analogous to the primes.
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REFERENCES
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Ado [Simone Caramel], Postings in egroups and newsgroups.
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LINKS
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T. D. Noe, Table of n, a(n) for n=0..500
Matthew M. Conroy, Home page (listed instead of email address)
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FORMULA
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G.f.: (1-3x+2x^2+x^3+x^4)/((x-1)^3 (x^2+x-1)) - T. D. Noe, Oct 12 2007
a(n) = 4a(n-1)-5a(n-2)+a(n-3)+2a(n-4)-a(n-5) - T. D. Noe, Oct 12 2007
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MAPLE
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a := proc(n) option remember: f := n->fibonacci(n+1): if n=0 then RETURN(1) fi: a(n-1)+2*(f(n)-n): end: for n from 1 to 60 do printf(`%d, `, a(n)) od:
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MATHEMATICA
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a[0] = f[0] = f[1] = 1; f[n_] := f[n] = f[n - 1] + f[n - 2]; a[n_] := a[n] = a[n - 1] + 2*(f[n] - n); Table[ a[n], {n, 0, 40} ]
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PROGRAM
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(ARIBAS): function a064551(maxarg: integer); var n, r, rm, q, qm1, qm2: integer; begin qm2 := 0; qm1 := 0; rm := 0; for n := 0 to maxarg do if n < 2 then q := 1; else q := qm1 + qm2; end; qm2 := qm1; qm1 := q; if n = 0 then r := 1; else r := rm + 2*(q - n); end; rm := r; write(r, " "); end; end; a064551(35).
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CROSSREFS
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Cf. A064550, A064552, A000045.
Sequence in context: A032284 A029512 A018555 this_sequence A005783 A045883 A133654
Adjacent sequences: A064548 A064549 A064550 this_sequence A064552 A064553 A064554
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KEYWORD
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nonn,nice,easy
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Oct 08 2001
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Matthew M. Conroy and James A. Sellers (sellersj(AT)math.psu.edu), Oct 10 2001
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