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Union of Fibonacci and triangular numbers.
1

%I #13 Aug 22 2019 17:42:19

%S 0,1,2,3,5,6,8,10,13,15,21,28,34,36,45,55,66,78,89,91,105,120,136,144,

%T 153,171,190,210,231,233,253,276,300,325,351,377,378,406,435,465,496,

%U 528,561,595,610,630,666,703,741,780,820,861,903,946,987,990,1035,1081

%N Union of Fibonacci and triangular numbers.

%H Harvey P. Dale, <a href="/A122493/b122493.txt">Table of n, a(n) for n = 0..1000</a>

%p #does not generate terms in order# with(combinat, fibonacci): for i from 1 to 20 do fibonacci(i); sum(k, k=0..i); end do;

%t Module[{upto=1100,f=1,tr},While[Fibonacci[f]<upto,f++];tr=Ceiling[ (Sqrt[ 1+8*upto]-1)/2];Select[Join[Fibonacci[Range[0,f]],Accumulate[ Range[ tr]]]// Union,#<=upto&]] (* _Harvey P. Dale_, Oct 21 2016 *)

%Y Cf. A000045, A000217.

%K nonn

%O 0,3

%A _Ben Paul Thurston_, Sep 16 2006

%E More terms from _Franklin T. Adams-Watters_, Sep 20 2006