cp's OEIS Frontend

A165999 Triangle read by rows: T(0,0) = 1, T(n,k) = T(n-1,k-1) + T(n-1,k) for n > 0, 0 < k <= trinv(n), where trinv(n) = floor((1+sqrt(1+8*n))/2), and entries outside triangle are 0.

%I A165999 #2 Mar 30 2012 17:28:33
%S A165999 1,1,1,1,2,1,3,2,1,4,5,1,5,9,1,6,14,9,1,7,20,23,1,8,27,43,1,9,35,70,1,
%T A165999 10,44,105,70,1,11,54,149,175,1,12,65,203,324,1,13,77,268,527,1,14,90,
%U A165999 345,795,1,15,104,435,1140,795,1,16,119,539,1575,1935,1,17,135,658,2114
%N A165999 Triangle read by rows: T(0,0) = 1, T(n,k) = T(n-1,k-1) + T(n-1,k) for n > 0, 0 < k <= trinv(n), where trinv(n) = floor((1+sqrt(1+8*n))/2), and entries outside triangle are 0.
%C A165999 There are trinv(n) terms in row n (see A002024). Related to A136730.
%e A165999 Triangle begins: [1] [1, 1] [1, 2] [1, 3, 2] [1, 4, 5] [1, 5, 9] [1, 6, 14, 9] [1, 7, 20, 23] [1, 8, 27, 43] [1, 9, 35, 70] [1, 10, 44, 105, 70] [1, 11, 54, 149, 175] [1, 12, 65, 203, 324] [1, 13, 77, 268, 527] [1, 14, 90, 345, 795] [1, 15, 104, 435, 1140, 795]
%o A165999 (PARI) trinv(n) = floor((1+sqrt(1+8*n))/2); f(n) = trinv(n-1); s=19;M=matrix(s,s);for(n=1,s,M[n,1]=1); for(n=2,s,for(k=2,f(n),M[n,k]=M[n-1,k-1]+M[n-1,k])); for(n=1,s,for(k=1,f(n),print1(M[n,k],", ")))
%Y A165999 A101482 (diagonal T(A000217(n), n))
%K A165999 nonn,tabf
%O A165999 0,5
%A A165999 _Gerald McGarvey_, Oct 03 2009