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 A210947 Triangle read by rows: T(n,k) = total number of parts <= k of all partitions of n. 6
 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 12, 16, 18, 19, 20, 19, 27, 31, 33, 34, 35, 30, 41, 47, 50, 52, 53, 54, 45, 64, 73, 79, 82, 84, 85, 86, 67, 93, 108, 116, 121, 124, 126, 127, 128, 97, 138, 159, 172, 180, 185, 188, 190, 191, 192 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Row n lists the partial sums of row n of triangle A066633. LINKS Alois P. Heinz, Rows n = 1..141, flattened FORMULA T(n,k) = Sum_{j=1..k} A066633(n,j). EXAMPLE Triangle begins: 1; 2, 3; 4, 5, 6; 7, 10, 11, 12; 12, 16, 18, 19, 20; 19, 27, 31, 33, 34, 35; 30, 41, 47, 50, 52, 53, 54; 45, 64, 73, 79, 82, 84, 85, 86; 67, 93, 108, 116, 121, 124, 126, 127, 128; MAPLE p:= (f, g)-> zip((x, y)-> x+y, f, g, 0): b:= proc(n, i) option remember; local f, g; if n=0 then [1] elif i=1 then [1, n] else f:= b(n, i-1); g:= `if`(i>n, [0], b(n-i, i)); p (p (f, g), [0\$i, g[1]]) fi end: T:= proc(n, k) option remember; b(n, n)[k+1] +`if`(k<2, 0, T(n, k-1)) end: seq (seq (T(n, k), k=1..n), n=1..11); # Alois P. Heinz, May 02 2012 MATHEMATICA p[f_, g_] := With[{m = Max[Length[f], Length[g]]}, PadRight[f, m, 0] + PadRight[g, m, 0]]; b[n_, i_] := b[n, i] = Module[{f, g}, If[n == 0, {1}, If[i == 1, {1, n}, f = b[n, i-1]; g = If[i>n, {0}, b[n-i, i]]; p[p[f, g], Append[Array[0&, i], g[[1]] ]]]]]; T[n_, k_] := T[n, k] = b[n, n][[k+1]] + If[k<2, 0, T[n, k-1]]; Table [Table [T[n, k], {k, 1, n}], {n, 1, 11}] // Flatten (* Jean-François Alcover, Mar 11 2015, after Alois P. Heinz *) CROSSREFS Column 1 is A000070(n-1). Right border gives A006128. Cf. A066633, A181187, A206563, A210948, A210955. Sequence in context: A362854 A102455 A073678 * A031981 A279486 A001476 Adjacent sequences: A210944 A210945 A210946 * A210948 A210949 A210950 KEYWORD nonn,tabl AUTHOR Omar E. Pol, May 01 2012 STATUS approved

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Last modified May 29 14:43 EDT 2024. Contains 372952 sequences. (Running on oeis4.)