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A143199 Triangle read by rows: T(n, m) = if m <= floor(n/2) then (n + 1)*a(m) + n otherwise (n + 1)*a(n - m) + n, where a(m) is A000096. 0
-1, -1, -1, -1, 2, -1, -1, 3, 3, -1, -1, 4, 14, 4, -1, -1, 5, 17, 17, 5, -1, -1, 6, 20, 41, 20, 6, -1, -1, 7, 23, 47, 47, 23, 7, -1, -1, 8, 26, 53, 89, 53, 26, 8, -1, -1, 9, 29, 59, 99, 99, 59, 29, 9, -1, -1, 10, 32, 65, 109, 164, 109, 65, 32, 10, -1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
LINKS
FORMULA
T(n, m) = (n + 1)*(if m <= floor(n/2) then (m - 1)*(m + 2) / 2 else (n - m + 2)*(n - (m + 1)) / 2 fi) + n. - Georg Fischer, Oct 28 2023
EXAMPLE
{-1},
{-1, -1},
{-1, 2, -1},
{-1, 3, 3, -1},
{-1, 4, 14, 4, -1},
{-1, 5, 17, 17, 5, -1},
{-1, 6, 20, 41, 20, 6, -1},
{-1, 7, 23, 47, 47, 23, 7, -1},
{-1, 8, 26, 53, 89, 53, 26, 8, -1},
{-1, 9, 29, 59, 99, 99, 59, 29, 9, -1},
{-1, 10, 32, 65, 109, 164, 109, 65, 32, 10, -1}
MAPLE
seq(print(seq((n + 1) * (if m <= n/2 then (m - 1) * (m + 2)\
/ 2 else (n - m + 2) * (n - (m + 1)) / 2 fi) + n, m=0..n)), n=0..10); # Georg Fischer, Oct 28 2023
MATHEMATICA
a[0] = -1; a[n_] := a[n] = a[n - 1] + n; Table[a[n], {n, 0, 30}]; t[n_, m_] := If[m <= Floor[n/2], (n + 1)*a[m] + n, (n + 1)*a[n - m] + n]; Table[Table[t[n, m], {m, 0, n}], {n, 0, 10}]//Flatten
CROSSREFS
Sequence in context: A059922 A229556 A159623 * A137896 A157219 A167040
KEYWORD
sign,tabl
AUTHOR
EXTENSIONS
Definition clarified and offset corrected by Georg Fischer, Oct 28 2023
STATUS
approved

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)