

A160504


a(n) = number of ordered pairs (i,j) such that a(i)+a(j)<n, i<j<n; a(1)=a(2)=1.


1



1, 1, 1, 3, 6, 6, 6, 15, 15, 18, 18, 18, 21, 21, 21, 21, 27, 27, 29, 38, 38, 47, 59, 59, 72, 72, 72, 84, 90, 90, 96, 96, 97, 109, 109, 112, 123, 123, 123, 141, 141, 143, 153, 153, 161, 167, 167, 170, 181, 181, 186, 186, 186, 193, 194, 194, 202, 202, 202, 210, 216, 216
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OFFSET

1,4


COMMENTS

It appears that the longest run of identical values in the sequence has length five, occurring twice: a(69) = ... = a(73) = 239 and a(81) = ... = a(85) = 282. Length four appears once at a(13) = ... = a(16) = 21. The last adjacent pair with equal values appears to be a(340) = a(341) = 2558; checked through n=1000.  Hartmut F. W. Hoft, Jun 04 2017


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..402


EXAMPLE

a(3) = 1 because there is only one possible pair of previous terms, {1, 1}, and its sum is 2, which is less than 3.
a(4) = 3 because there are three possible pairs of previous terms {a(1), a(2)}, {a(1), a(3)}, {a(2), a(3)}, which are here considered distinct even though they all work out to {1, 1} with a sum of 2, which is less than 4.
a(5) = 6 because there are six possible pairs of previous terms: {a(1), a(2)}, {a(1), a(3)}, {a(1), 3}, {a(2), a(3)}, {a(2), 3}, {a(3), 3}, with sums 2, 2, 4, 2, 4, 4, respectively, all of which are less than 6.


MATHEMATICA

count[cL_] := Module[{n=Length[cL]+1, c=0, i, j}, Do[If[cL[[i]]+cL[[j]]<n, c++], {j, 2, n1}, {i, j1}]; c]
a160504[n_] := Nest[Append[#, count[#]]&, {1, 1}, n]
a160504[60] (* data *)
(* Hartmut F. W. Hoft, Jun 04 2017 *)


CROSSREFS

Sequence in context: A295559 A161645 A081289 * A291801 A227501 A294981
Adjacent sequences: A160501 A160502 A160503 * A160505 A160506 A160507


KEYWORD

nonn


AUTHOR

Masahiko Shin, May 16 2009


EXTENSIONS

There were nonASCII characters in the definition, which I hope I have interpreted correctly!  N. J. A. Sloane, Jul 23 2009
Definition corrected by Sean A. Irvine, Apr 08 2010
Corrected and extended by Sean A. Irvine, Apr 08 2010


STATUS

approved



