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 A222404 Triangle read by rows: left and right edges are A002378, interior entries are filled in using the Pascal triangle rule. 3
 0, 2, 2, 6, 4, 6, 12, 10, 10, 12, 20, 22, 20, 22, 20, 30, 42, 42, 42, 42, 30, 42, 72, 84, 84, 84, 72, 42, 56, 114, 156, 168, 168, 156, 114, 56, 72, 170, 270, 324, 336, 324, 270, 170, 72, 90, 242, 440, 594, 660, 660, 594, 440, 242, 90, 110, 332, 682, 1034, 1254, 1320, 1254, 1034, 682, 332, 110 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS EXAMPLE Triangle begins: 0 2, 2 6, 4, 6 12, 10, 10, 12 20, 22, 20, 22, 20 30, 42, 42, 42, 42, 30 42, 72, 84, 84, 84, 72, 42 56, 114, 156, 168, 168, 156, 114, 56 ... MAPLE d:=[seq(n*(n+1), n=0..14)]; f:=proc(d) local T, M, n, i; M:=nops(d); T:=Array(0..M-1, 0..M-1); for n from 0 to M-1 do T[n, 0]:=d[n+1]; T[n, n]:=d[n+1]; od: for n from 2 to M-1 do for i from 1 to n-1 do T[n, i]:=T[n-1, i-1]+T[n-1, i]; od: od: lprint("triangle:"); for n from 0 to M-1 do lprint(seq(T[n, i], i=0..n)); od: lprint("row sums:"); lprint([seq( add(T[i, j], j=0..i), i=0..M-1)]); end; f(d); MATHEMATICA t[n_, n_] := n*(n+1); t[n_, 0] := n*(n+1); t[n_, k_] := t[n, k] = t[n-1, k-1] + t[n-1, k]; Table[t[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jan 20 2014 *) CROSSREFS Cf. A007318, A002378, A222403, A222405. Row sums are 4*A000295. Sequence in context: A036500 A077080 A273012 * A081111 A092686 A249796 Adjacent sequences:  A222401 A222402 A222403 * A222405 A222406 A222407 KEYWORD nonn,tabl AUTHOR N. J. A. Sloane, Feb 18 2013 STATUS approved

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Last modified December 8 01:42 EST 2019. Contains 329850 sequences. (Running on oeis4.)