1,2

The n-th row of the triangular table begins by considering n triangular numbers (A000217) in order. Now segregate them into n groups beginning with n members in the first group, n-1 members in the second group, etc. Now sum each group. Thus the first term is the sum of first n numbers = n(n+1)/2, the second term is the sum of the next n-1 terms (from n+1 to 2n-1), the third term is the sum of the next n-2 terms (2n to 3n-3), etc. and the last term is simply n(n+1)/2. This triangle can be called as triangular triangle. The sequence contains the triangle by rows.

T(n) is the n-th Triangular number = C(n+1, 2) = n(n+1)/2 = 0+1+2+...+n. TT(n, k) is the k-th term of the n-th row, 0<k<=n.

TT(n, k) = T(k*n - T(k - 1)) - T((k - 1)*n - T(k - 2)).

1

3, 3

6, 9, 6

10, 18, 17, 10

15, 30, 33, 27, 15

21, 45, 54, 51, 39, 21

28, 63, 80, 82, 72, 53, 28

36, 84, 111, 120, 114, 96, 69, 36

The row for n = 4 is (1+2+3+4), (5+6+7), (8+9), 10 => 10 18 17 10.

T[n_] := n(n + 1)/2; TT[n_, k_] := T[k*n - T[k - 1]] - T[(k - 1)*n - T[k - 2]]; Flatten[ Table[ TT[n, k], {n, 1, 11}, {k, 1, n}]] (from Robert G. Wilson v Apr 24 2004)

Cf. A093446. TT(n, 1) = TT(n, n) = T(n) = A000217. TT(n, 2) = A045943. TT(n, n-1) = A014209. TT(0, k) = A027480.

Sequence in context: A104715 A164743 A110769 this_sequence A098358 A136289 A128012

Adjacent sequences: A093442 A093443 A093444 this_sequence A093446 A093447 A093448

nonn,nice,tabl

Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Apr 02 2004

Edited, corrected and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 24 2004