OFFSET
0,2
COMMENTS
Offset for r (the rows) is 1, for s (the columns) it is 0.
LINKS
G. C. Greubel, Rows n = 0..100 of triangle, flattened
FORMULA
T(r, s) = r*(2*r^2 + 3*r - 3*r*s + 1 + 3*s^2)/6, r >= 1, 0 <= s <= r-1.
EXAMPLE
Triangle begins as:
1;
5, 4;
14, 11, 11;
30, 24, 22, 24;
55, 45, 40, 40, 45;
91, 76, 67, 64, 67, 76;
MAPLE
T:=proc(r, s) if s>=r then 0 else r*(2*r^2+3*r+1-3*r*s+3*s^2)/6 fi end: for r from 1 to 11 do seq(T(r, s), s=0..r-1) od; # yields sequence in triangular form # Emeric Deutsch, Nov 27 2006
MATHEMATICA
Table[n*((n+1)*(2*n+1) -3*k*(n-k))/6, {n, 0, 12}, {k, 0, n-1}]//Flatten (* G. C. Greubel, Oct 30 2019 *)
PROG
(PARI) T(n, k) = n*((n+1)*(2*n+1) -3*k*(n-k))/6;
for(n=0, 12, for(k=0, n-1, print1(T(n, k), ", "))) \\ G. C. Greubel, Oct 30 2019
(Magma) [n*((n+1)*(2*n+1) -3*k*(n-k))/6: k in [0..n-1], n in [0..12]]; // G. C. Greubel, Oct 30 2019
(Sage) [[n*((n+1)*(2*n+1) -3*k*(n-k))/6 for k in (0..n-1)] for n in (0..12)] # G. C. Greubel, Oct 30 2019
(GAP) Flat(List([0..12], n-> List([0..n-1], k-> n*((n+1)*(2*n+1) -3*k*(n-k))/6 ))); # G. C. Greubel, Oct 30 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Ralf Stephan, May 02 2004
EXTENSIONS
More terms from G. C. Greubel, Oct 30 2019
STATUS
approved