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 A121512 a(n) = a(n-1) + a(n-3) - a(n-4) for n>4, with a(1)=1, a(2)=4, a(3)=10, a(4)=4. 0
 1, 4, 10, 4, 7, 13, 7, 10, 16, 10, 13, 19, 13, 16, 22, 16, 19, 25, 19, 22, 28, 22, 25, 31, 25, 28, 34, 28, 31, 37, 31, 34, 40, 34, 37, 43, 37, 40, 46, 40, 43, 49, 43, 46, 52, 46, 49, 55, 49, 52, 58, 52, 55, 61, 55, 58, 64, 58, 61, 67, 61, 64, 70, 64, 67, 73 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This sequence gives a linearly increasing triangle shaped form on plotting. LINKS Table of n, a(n) for n=1..66. Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1). FORMULA G.f.: -x*(-1-3*x-6*x^2+7*x^3)/((1+x+x^2)*(x-1)^2). [Oct 14 2009] a(n) = n+3 + (-1)^n * A130806(n+1). [Oct 14 2009] a(n) = (24*n + 75 - 18*cos(2*(n+1)*Pi/3) + 9*cos(2*Pi*sin(2*n*Pi/3)/sqrt(3)) + 50*sqrt(3)*sin(2*(n+1)*Pi/3))/24. - Wesley Ivan Hurt, Oct 05 2017 MATHEMATICA M = {{0, 1, 0}, {0, 0, 1}, {1, 0, 0}} v[1] = {1, 4, 10} v[n_] := v[n] = M.v[n - 1] + {0, 0, 3} a = Table[v[n][[1]], {n, 1, 50}] CROSSREFS Cf. A005448, A130806. Sequence in context: A070261 A367029 A054048 * A291527 A010715 A151707 Adjacent sequences: A121509 A121510 A121511 * A121513 A121514 A121515 KEYWORD nonn,easy AUTHOR Roger L. Bagula, Sep 07 2006 EXTENSIONS Definition replaced by recurrence - The Assoc. Editors of the OEIS, Oct 14 2009 STATUS approved

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Last modified July 19 17:03 EDT 2024. Contains 374410 sequences. (Running on oeis4.)