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 A135997 Table of triples T(k,m) = k (m=1), 2-k (m=2) and 1-k (m=3). 2
 0, 2, 1, 1, 1, 0, 2, 0, -1, 3, -1, -2, 4, -2, -3, 5, -3, -4, 6, -4, -5, 7, -5, -6, 8, -6, -7, 9, -7, -8, 10, -8, -9, 11, -9, -10, 12, -10, -11, 13, -11, -12, 14, -12, -13, 15, -13, -14, 16, -14, -15, 17, -15, -16, 18, -16, -17, 19, -17, -18, 20, -18, -19, 21, -19, -20, 22, -20, -21, 23 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The table comprises recurrence coefficients for Fibonacci-related sequences b_k(n) = Sum_{m=1..3} T(k,m)*b_k(n-m). The first row coefficients (0,2,1) are used in A008346, b(n)=2b(n-2)+b(n-3), for example. The 2nd row coefficients (1,1,0) represent b(n)=b(n-1)+b(n-2) of A000045, for example. The 3rd row coefficients (2,0,-1) are used in A001611, A020706 and Pisot sequences like A018910. The 4th row coefficients (3,-1,-2) are used in A052550, A052911, A074878 or A088859, for example. LINKS Michael De Vlieger, Table of n, a(n) for n = 0..9002 (rows 1 <= k <= 3000) FORMULA Row sums: Sum_{m=1..3} T(k,m) = A022959(k). a(n) = (3*n-12+12*cos(2*n*Pi/3)-2*sqrt(3)*sin(2*n*Pi/3))*(-1)^sign(n mod 3))/9. - Wesley Ivan Hurt, Oct 01 2017 EXAMPLE The table has 3 columns and starts: 0, 2, 1; 1, 1, 0; 2, 0,-1; 3,-1,-2; MATHEMATICA Array[{#, 2 - #, 1 - #} &, 24, 0] // Flatten (* Michael De Vlieger, Oct 01 2017 *) CROSSREFS Cf. A022959. Sequence in context: A214021 A260516 A064744 * A026609 A286935 A090340 Adjacent sequences: A135994 A135995 A135996 * A135998 A135999 A136000 KEYWORD sign,tabf,less,easy AUTHOR Paul Curtz, Mar 03 2008 EXTENSIONS Edited and extended by R. J. Mathar, Jul 22 2008 STATUS approved

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Last modified October 1 14:44 EDT 2023. Contains 365826 sequences. (Running on oeis4.)