A159924 Triangle read by rows: a(m,m) = 1, for all m. For n < m, a(m,n) = a(m-1,n) + (sum of all terms in rows 1 through m-1).

1, 2, 1, 6, 5, 1, 22, 21, 17, 1, 99, 98, 94, 78, 1, 546, 545, 541, 525, 448, 1, 3599, 3598, 3594, 3578, 3501, 3054, 1, 27577, 27576, 27572, 27556, 27479, 27032, 23979, 1, 240327, 240326, 240322, 240306, 240229, 239782, 236729, 212751, 1, 2343850

Offset: 1

Author

Leroy Quet, Apr 26 2009

Keywords

• nonn
• tabl

Comments

Row sums are A159925. Sum of all terms in rows 1 through m is A159926(m). A159926(m) - A159926(m-1) = A159925(m), for m >= 2.

Examples

			The triangle starts like this:
1,
2,1,
6,5,1,
22,21,17,1
The sum of all these terms is 77. So adding 77 to each of the terms of the 4th row gets the fifth row: 22+77=99, 21+77=98, 17+77=94, 1+77=78, and the final terms is set at 1. So row 5 is: 99,98,94,78,1.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..11476 (rows 1 <= n <= 150).

Crossrefs

Cf. A159925, A159926, A159927.

Programs

Maple

A159924 := proc(n,m) option remember ; local s; if n = m then 1; else s := add(add(procname(r,c),c=1..r),r=1..n-1) ; procname(n-1,m)+s ; fi; end: for n from 1 to 13 do for m from 1 to n do printf("%d,",A159924(n,m)) ; od: od: # R. J. Mathar, Apr 29 2009

Mathematica

Block[{m = 0}, NestList[Block[{w = #}, AddTo[m, Total@ w]; Append[m + w, 1]] &, {1}, 9]] // Flatten (* Michael De Vlieger, Sep 23 2017 *)

Extensions

More terms from R. J. Mathar, Apr 29 2009