

A227353


Number of lattice points in the closed region bounded by the graphs of y = 3*x/5, x = n, and y = 0, excluding points on the xaxis.


2



0, 1, 2, 4, 7, 10, 14, 18, 23, 29, 35, 42, 49, 57, 66, 75, 85, 95, 106, 118, 130, 143, 156, 170, 185, 200, 216, 232, 249, 267, 285, 304, 323, 343, 364, 385, 407, 429, 452, 476, 500, 525, 550, 576, 603, 630, 658, 686, 715, 745, 775, 806, 837, 869, 902, 935
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OFFSET

1,3


COMMENTS

See A227347.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (2, 1, 0, 0, 1, 2, 1).


FORMULA

a(n) = 2*a(n1)  a(n2) + a(n5)  2a(n6) + a(n7).
G.f.: (x (1 + x^2 + x^3))/((1  x)^3 (1 + x + x^2 + x^3 + x^4)).


EXAMPLE

a(1) = floor(3/5) = 0; a(2) = floor(6/5) = 1; a(3) = a(2) + floor(9/5) = 2; a(4) = a(2) + a(3) + floor(12/5) = 4.


MATHEMATICA

z = 150; r = 3/5; k = 1; a[n_] := Sum[Floor[r*x^k], {x, 1, n}]; t = Table[a[n], {n, 1, z}]


CROSSREFS

Cf. A227347, A130520, A011858, A033437.
Sequence in context: A194244 A014616 A184674 * A183136 A144873 A120679
Adjacent sequences: A227350 A227351 A227352 * A227354 A227355 A227356


KEYWORD

nonn,easy


AUTHOR

Clark Kimberling, Jul 08 2013


STATUS

approved



