A085930 Triangle read by rows in which row n contains n smallest (> 0) numbers which when incremented by n yield a triangular number.

2, 1, 4, 3, 7, 12, 2, 6, 11, 17, 1, 5, 10, 16, 23, 4, 9, 15, 22, 30, 39, 3, 8, 14, 21, 29, 38, 48, 2, 7, 13, 20, 28, 37, 47, 58, 1, 6, 12, 19, 27, 36, 46, 57, 69, 5, 11, 18, 26, 35, 45, 56, 68, 81, 95, 4, 10, 17, 25, 34, 44, 55, 67, 80, 94, 109, 3, 9, 16, 24, 33, 43, 54, 66, 79, 93, 108, 124

Offset

1,1

Comments

Row n contains n terms.

Links

Gheorghe Coserea, Rows n = 1..201, flattened

Formula

T(n, k) = A000217(k+A003056(n))-n. - David Wasserman, Feb 23 2004

Example

For n = 4 we have row 4 with 2, 6, 11, 17 since 2 + 4 = 3*4/2, 6 + 4 = 4*5/2, 11 + 4 = 5*6/2, 17 + 4 = 6*7/2.
Triangle starts:
n\k  [1]   [2]   [3]   [4]   [5]   [6]   [7]   [8]   [9]   [10]  [11]
[1]  2;
[2]  1,    4;
[3]  3,    7,    12;
[4]  2,    6,    11,   17;
[5]  1,    5,    10,   16,   23;
[6]  4,    9,    15,   22,   30,   39;
[7]  3,    8,    14,   21,   29,   38    48;
[8]  2,    7,    13,   20,   28,   37,   47,   58;
[9]  1,    6,    12,   19,   27,   36,   46,   57,   69;
[10] 5,    11,   18,   26,   35,   45,   56,   68,   81,   95;
[11] 4,    10,   17,   25,   34,   44,   55,   67,   80,   94,   109;
[12] ...

Prog

(PARI)
t(n, k) = my(x = (sqrtint(1+8*n)-1)\2); (x+k)*(x+k+1)/2 - n;
concat(vector(12, n, vector(n, k, t(n, k))))  \\ Gheorghe Coserea, Mar 25 2016

Crossrefs

Cf. A000217.

Sequence in context: A109250 A138236 A058354 * A258863 A087207 A179206

Adjacent sequences: A085927 A085928 A085929 * A085931 A085932 A085933

Keyword

easy,nonn,tabl

Author

Amarnath Murthy and Jason Earls, Jul 14 2003

Extensions

Offset corrected by Gheorghe Coserea, Mar 25 2016

Status

approved