Original entry on oeis.org
1, 3, 12, 61, 370, 2606, 20925, 188772, 1890773, 20822481, 250082522, 3253176309, 45567394330, 683783923476, 10944068960451, 186098265906832, 3350501663825617, 63671208559149815, 1273621946395366224
Offset: 1
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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: A159925 := proc(n) local m; add( A159924(n,m),m=1..n) ; end: seq(A159925(n),n=1..40) ; # R. J. Mathar, Apr 29 2009
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Total /@ Block[{m = 0}, NestList[Block[{w = #}, AddTo[m, Total@ w]; Append[m + w, 1]] &, {1}, 18]] (* Michael De Vlieger, Oct 30 2017 *)
A159926
The sum of all terms in row 1 through m of triangle A159924.
Original entry on oeis.org
1, 4, 16, 77, 447, 3053, 23978, 212750, 2103523, 22926004, 273008526, 3526184835, 49093579165, 732877502641, 11676946463092, 197775212369924, 3548276876195541, 67219485435345356, 1340841431830711580
Offset: 1
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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: A159925 := proc(n) local m; add( A159924(n,m),m=1..n) ; end: A159926 := proc(n) add( A159925(k),k=1..n) ; end: seq(A159926(n),n=1..40) ; # R. J. Mathar, Apr 29 2009
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Accumulate@ Map[Total, Block[{m = 0}, NestList[Block[{w = #}, AddTo[m, Total@ w]; Append[m + w, 1]] &, {1}, 18]]] (* Michael De Vlieger, Oct 30 2017 *)
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.
Original entry on oeis.org
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
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.
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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
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NestList[{#1 + #2, #2} & @@ {Join[#1, {0}], Total[#1] + #2} & @@ # &, {{1}, 0}, 8][[All, 1]] // Flatten (* Michael De Vlieger, Aug 30 2017 *)
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