|
%I #43 Nov 01 2021 04:55:37
%S 0,1,2,3,2,3,4,5,6,3,4,5,6,7,8,9,4,5,6,7,8,9,10,11,12,5,6,7,8,9,10,11,
%T 12,13,14,15,6,7,8,9,10,11,12,13,14,15,16,17,18,7,8,9,10,11,12,13,14,
%U 15,16,17,18,19,20,21
%N Triangle read by rows: T(n,k) = n+k with 0 <= k <= 2*n.
%C The left half together with the central column is the A051162 triangle.
%C Row sums of the reciprocals of the terms in the above triangle converge to log(3). See link to Eric Naslund's answer. [_Mats Granvik_, Apr 07 2013]
%C The first time that the numbers of the triplet 3k+1, 3k+2, 3k+3 appear in the sequence is for a(k^2+4*k+1) = 3*k+1, a(k^2+4*k+2) = 3*k+2, a(k^2+4*k+3) = 3*k+3 for k >= 0. - _Bernard Schott_, Jun 09 2019
%H Eric Naslund, <a href="http://math.stackexchange.com/questions/46713/euler-mascheroni-constant-expression-further-simplification/46718#46718">Euler-Mascheroni constant expression, further simplification</a>
%F a(n) = floor(sqrt(n)) - floor(sqrt(n))^2 + n. - _Ridouane Oudra_, Jun 08 2019
%e Triangle begins:
%e 0
%e 1 2 3
%e 2 3 4 5 6
%e 3 4 5 6 7 8 9
%e 4 5 6 7 8 9 10 11 12
%e 5 6 7 8 9 10 11 12 13 14 15
%e 6 7 8 9 10 11 12 13 14 15 16 17 18
%e 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21
%p seq(seq(n+k, k=0..2*n), n=0..12); # _Ridouane Oudra_, Jun 08 2019
%Y Cf. A051162, A094727.
%K nonn,tabf,easy
%O 0,3
%A _Alex Ratushnyak_, Mar 12 2013
|
