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 A279100 a(n) = Sum_{k=0..n} ceiling(phi^k), where phi is the golden ratio (A001622). 0
 1, 3, 6, 11, 18, 30, 48, 78, 125, 202, 325, 525, 847, 1369, 2212, 3577, 5784, 9356, 15134, 24484, 39611, 64088, 103691, 167771, 271453, 439215, 710658, 1149863, 1860510, 3010362, 4870860, 7881210, 12752057, 20633254, 33385297, 54018537, 87403819, 141422341, 228826144, 370248469, 599074596 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Partial sums of A169986. LINKS Eric Weisstein's World of Mathematics, Golden Ratio Index entries for linear recurrences with constant coefficients, signature (2,1,-3,0,1). FORMULA G.f.: (1 + x - x^2 - x^3 - x^4)/((1 - x)^2*(1 - 2*x^2 - x^3)). a(n) = 2*a(n-1) + a(n-2) - 3*a(n-3) + a(n-5). a(n) = (10*n - 5*(-1)^n + 2^(1-n)*sqrt(5)*(5 + 3*sqrt(5))*(1 + sqrt(5))^n + sqrt(5)*2^(1-n)*(3*sqrt(5) - 5) *(1 - sqrt(5))^n - 35)/20. a(n) ~ phi^(n+2). MATHEMATICA Accumulate[Table[Ceiling[GoldenRatio^n], {n, 0, 40}]] LinearRecurrence[{2, 1, -3, 0, 1}, {1, 3, 6, 11, 18}, 41] CROSSREFS Cf. A001622, A020956, A169986. Sequence in context: A152074 A123629 A212484 * A053992 A052825 A003082 Adjacent sequences:  A279097 A279098 A279099 * A279101 A279102 A279103 KEYWORD nonn,easy AUTHOR Ilya Gutkovskiy, Dec 06 2016 STATUS approved

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Last modified September 21 19:57 EDT 2020. Contains 337273 sequences. (Running on oeis4.)