Search: id:A002262
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%I A002262
%S A002262 0,0,1,0,1,2,0,1,2,3,0,1,2,3,4,0,1,2,3,4,5,0,1,2,3,4,5,6,0,1,2,3,4,
%T A002262 5,6,7,0,1,2,3,4,5,6,7,8,0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,10,
%U A002262 0,1,2,3,4,5,6,7,8,9,10,11,0,1,2,3,4,5,6,7,8,9,10,11,12,0,1,2,3,4,5
%N A002262 Integers 0 to n followed by integers 0 to n+1 etc.
%C A002262 a(n) = n - the largest triangular number <= n. - Amarnath Murthy (amarnath_murthy(AT)yahoo.com), 
               Dec 25 2001
%C A002262 The PARI functions t1, t2 can be used to read a square array T(n,k) (n 
               >= 0, k >= 0) by antidiagonals downwards: n -> T(t1(n), t2(n)). - 
               Michael Somos, Aug 23, 2002
%C A002262 Values x of unique solution pair (x,y) to equation T(x+y) + x = n, where 
               T(k)=A000217(k). - Lekraj Beedassy (blekraj(AT)yahoo.com), Aug 21 
               2004
%C A002262 a(A000217(n)) = 0; a(A000096(n)) = n. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               May 20 2009]
%H A002262 M. Somos, <a href="a073189.txt">Sequences used for indexing triangular 
               or square arrays</a>
%F A002262 a(n) = (n-((trinv(n)*(trinv(n)-1))/2)); trinv := n -> floor((1+sqrt(1+8*n))/
               2) (cf. A002024); # Gives integral inverses of triangular numbers.
%F A002262 a(n)=n-A000217(A003056(n))=n-A057944(n). - Lekraj Beedassy (blekraj(AT)yahoo.com), 
               Aug 21 2004
%F A002262 a(n) = A140129(A023758(n+2)). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               May 14 2008
%F A002262 a(n)=f(n,1) with f(n,m) = if n<m then n else f(n-m,m+1). [From Reinhard 
               Zumkeller (reinhard.zumkeller(AT)gmail.com), May 20 2009]
%p A002262 A002262 := n -> n - binomial(floor((1/2)+sqrt(2*(1+n))),2);
%o A002262 (PARI) a(n)=n-binomial(floor(1/2+sqrt(2+2*n)),2)
%o A002262 (PARI) t1(n)=n-binomial(floor(1/2+sqrt(2+2*n)),2) /* A002262 */
%o A002262 (PARI) t2(n)=binomial(floor(3/2+sqrt(2+2*n)),2)-(n+1) /* A025581 */
%Y A002262 A002260(n)=1+a(n).
%Y A002262 Cf. A025675, A025682, A025691, A002024, A048645, A004736, A025581. As 
               a sequence, essentially same as A048151.
%Y A002262 A053645, A053186. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               May 20 2009]
%Y A002262 Sequence in context: A025690 A025668 A048151 this_sequence A025675 A025682 
               A025691
%Y A002262 Adjacent sequences: A002259 A002260 A002261 this_sequence A002263 A002264 
               A002265
%K A002262 nonn,tabl,easy,nice
%O A002262 0,6
%A A002262 Angele Hamel (amh(AT)maths.soton.ac.uk)

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