A159927 Triangle read by rows: a(1,1) = 1. a(m,m) = sum of all terms in rows 1 through m-1. a(m,n) = a(m-1,n) + (sum of all terms in rows 1 through m-1), for n < m.

1, 2, 1, 6, 5, 4, 25, 24, 23, 19, 135, 134, 133, 129, 110, 886, 885, 884, 880, 861, 751, 6784, 6783, 6782, 6778, 6759, 6649, 5898, 59115, 59114, 59113, 59109, 59090, 58980, 58229, 52331, 576527, 576526, 576525, 576521, 576502, 576392, 575641, 569743

Offset: 1

Author

Leroy Quet, Apr 26 2009

Keywords

• nonn
• tabl

Comments

A159928(m) = -A075374(m+4)+A075374(m+3), for m >= 1. -A075374(m+4) = the sum of all terms of triangle A159927 in rows 1 through m. A159928 contains the row-sums of triangle A159927.

Examples

			The triangle starts like this:
   1;
   2,  1;
   6,  5,  4;
  25, 24, 23, 19;
The sum of all of these terms is 110. Adding 110 to each term of the 4th row, we get: 25+110=135, 24+110=134, 23+110=133, 19+110=129, 0+110=110. So row 5 is 135,134,133,129,110.
		

Links

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

Crossrefs

Cf. A159924, A159928, A075374.

Programs

Maple

A159927 := proc(n,m) option remember; local rs; if n = 1 then 1; else rs := add(add( procname(i,j),j=1..i),i=1..n-1) ; if n = m then rs; else procname(n-1,m)+rs; fi; fi; end: for n from 1 to 10 do for m from 1 to n do printf("%d,",A159927(n,m)) ; od: od: # R. J. Mathar, Apr 28 2009

Mathematica

NestList[{#1 + #2, #2} & @@ {Join[#1, {0}], Total[#1] + #2} & @@ # &, {{1}, 0}, 8][[All, 1]] // Flatten (* Michael De Vlieger, Aug 30 2017 *)

Extensions

More terms from R. J. Mathar, Apr 28 2009