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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. 5
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

LINKS

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

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A159924, A159928, A075374.

Sequence in context: A346306 A021826 A331435 * A176443 A105225 A011018

Adjacent sequences:  A159924 A159925 A159926 * A159928 A159929 A159930

KEYWORD

nonn,tabl

AUTHOR

Leroy Quet, Apr 26 2009

EXTENSIONS

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

STATUS

approved

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Last modified May 29 01:41 EDT 2022. Contains 354122 sequences. (Running on oeis4.)