OFFSET
1,3
LINKS
Alois P. Heinz, Rows n = 1..100, flattened
Wikipedia, Standard deviation
EXAMPLE
Triangle T(n,k) begins:
1;
1;
2;
1, 1;
2, 1;
2, 1, 1;
2, 2, 1;
1, 3, 1, 1;
3, 2, 2, 1;
1, 4, 3, 1, 1;
2, 4, 3, 2, 1;
2, 4, 5, 2, 1, 1;
MAPLE
b:= proc(n, i, m, s, c) `if`(n>i*(i+1)/2, 0, `if`(n=0,
x^floor(sqrt(s/c-(m/c)^2)), b(n, i-1, m, s, c)+
`if`(i>n, 0, b(n-i, i-1, m+i, s+i^2, c+1))))
end:
T:= n->(p->seq(coeff(p, x, i), i=0..degree(p)))(b(n$2, 0$3)):
seq(T(n), n=1..20);
MATHEMATICA
b[n_, i_, m_, s_, c_] := If[n > i*(i + 1)/2, 0, If[n == 0, x^Floor[Sqrt[ s/c - (m/c)^2]], b[n, i - 1, m, s, c] + If[i > n, 0, b[n - i, i - 1, m + i, s + i^2, c + 1]]]];
T[n_] := Table[Coefficient[#, x, i], {i, 0, Exponent[#, x]}]&[b[n, n, 0, 0, 0]];
Table[T[n], {n, 1, 20}] // Flatten (* Jean-François Alcover, May 22 2018, translated from Maple *)
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Alois P. Heinz, Mar 12 2014
STATUS
approved