OFFSET
1,2
LINKS
G. C. Greubel, Rows n = 1..100 of triangle, flattened
FORMULA
From Werner Schulte, Feb 12 2019: (Start)
G.f.: Sum_{n>0,k=1..n} T(n,k)*x^k*t^n = x*t*((1-t+2*t^2)*(1-x*t) + (1-t)*t)/((1-t)^3*(1-x*t)^2).
Row sums: Sum_{k=1..n} T(n,k) = A006000(n-1) for n > 0.
Recurrence: T(n,k) = T(n,k-1) - n for 1 < k <= n with initial values T(n,1) = n^2-n+1 for n > 0.
Recurrence: T(n,k) = T(n-1,k) + 2*n-k-1 for 1 <= k < n with initial values T(n,n) = 1 for n > 0.
(End)
EXAMPLE
Triangle begins:
n\k: 1 2 3 4 5 6 7 8 9 10 11 12
====================================================
1: 1
2: 3 1
3: 7 4 1
4: 13 9 5 1
5: 21 16 11 6 1
6: 31 25 19 13 7 1
7: 43 36 29 22 15 8 1
8: 57 49 41 33 25 17 9 1
9: 73 64 55 46 37 28 19 10 1
10: 91 81 71 61 51 41 31 21 11 1
11: 111 100 89 78 67 56 45 34 23 12 1
12: 133 121 109 97 85 73 61 49 37 25 13 1
etc.
MATHEMATICA
Table[1+n*(n-k), {n, 12}, {k, n}]//Flatten
PROG
(PARI) {T(n, k) = 1+n*(n-k)}; \\ G. C. Greubel, Apr 22 2019
(Magma) [[1+n*(n-k): k in [1..n]]: n in [1..12]]; // G. C. Greubel, Apr 22 2019
(Sage) [[1+n*(n-k) for k in (1..n)] for n in (1..12)] # G. C. Greubel, Apr 22 2019
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Feb 10 2019
STATUS
approved