

A173276


a(n) = a(n2) + a(n3)  floor(a(n3)/2)  floor(a(n4)/2).


1



1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 8, 8, 9, 9, 9, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 19, 19, 19, 20, 20, 21, 21, 21, 22, 22, 23, 23, 23, 24, 24, 25, 25, 25, 26, 26, 27, 27, 27, 28, 28
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OFFSET

0,4


COMMENTS

Instead of the Fibonacci sequence this has the base Padovan sequence.
The a(n+1)/a(n) ratio approaches one.


LINKS

Table of n, a(n) for n=0..69.
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,1,1).


FORMULA

a(n) = a(n2)+a(n3)floor(a(n3)/2)floor(a(n4)/2).
Empirical g.f.: (x^3+1) / (x^6x^5x+1) = (x+1)*(x^2x+1) / ((x1)^2*(x^4+x^3+x^2+x+1)).  Colin Barker, Mar 23 2013
From Wesley Ivan Hurt, Mar 15 2015: (Start)
a(n) = a(n1) + a(n5)  a(n6).
a(n) = floor( (2n+5)/5 ). (End)


MAPLE

A173276:=n>floor((2*n+5)/5): seq(A173276(n), n=0..50); # Wesley Ivan Hurt, Mar 15 2015


MATHEMATICA

f[2] = 0; f[1] = 0; f[0] = 1; f[1] = 1;
f[n_] := f[n] = f[n  2] + f[n  3]  Floor[f[n  3]/2]  Floor[f[n  4]/2]
Table[f[n], {n, 0, 50}]


PROG

(MAGMA) [Floor((2*n+5)/5) : n in [0..50]]; // Wesley Ivan Hurt, Mar 15 2015
(PARI) vector(100, n, (2*n+3)\5) \\ Derek Orr, Mar 21 2015


CROSSREFS

Cf. A000931 (Padovan), A085269.
Sequence in context: A057362 A214046 A085269 * A288156 A248515 A194986
Adjacent sequences: A173273 A173274 A173275 * A173277 A173278 A173279


KEYWORD

nonn,easy


AUTHOR

Roger L. Bagula, Nov 22 2010


STATUS

approved



