OFFSET
0,3
COMMENTS
Distinct members (except 0) are in A071562. Numbers occurring at least twice are in A175040. - Franklin T. Adams-Watters, Apr 04 2010
FORMULA
T(n,0) = A000290(n).
T(n,1) = A002378(n) for n > 0.
T(n,2) = A005563(n) for n > 1.
T(n,3) = A028552(n) for n > 2.
T(n,4) = A028347(n+2) for n > 3.
T(n,5) = A028557(n) for n > 4.
T(n,6) = A028560(n) for n > 5.
T(n,7) = A028563(n) for n > 6.
T(n,8) = A028566(n) for n > 7.
T(n,9) = A028569(n) for n > 8.
T(n,10) = A098603(n) for n > 9.
T(n,n-5) = A071355(n-4) for n > 4.
T(n,n-4) = A054000(n-1) for n > 3.
T(n,n-3) = A014107(n) for n > 2.
T(n,n-2) = A046092(n-1) for n > 1.
T(n,n-1) = A000384(n) for n > 0.
T(n,n) = A001105(n).
Row sums give A085789 for n > 0.
G.f.: x*(1 + 2*y + 6*x^3*y^2 - 3*x^2*y*(1 + 2*y) + x*(1 - 3*y + 2*y^2))/((1 - x)^3*(1 - x*y)^3). - Stefano Spezia, Jul 03 2025
EXAMPLE
Triangle begins:
0
1 2
4 6 8
9 12 15 18
16 20 24 28 32
25 30 35 40 45 50
36 42 48 54 60 66 72
49 56 63 70 77 84 91 98
64 72 80 88 96 104 112 120 128
MATHEMATICA
Table[n(n+k), {n, 0, 10}, {k, 0, n}]//Flatten (* Harvey P. Dale, Aug 16 2018 *)
PROG
(PARI) row(n) = vector(n+1, k, n*(n+k-1)); \\ Amiram Eldar, May 09 2025
CROSSREFS
KEYWORD
AUTHOR
Reinhard Zumkeller, Nov 18 2004
STATUS
approved
