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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

%I

%S 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,

%T 84,72,42,56,114,156,168,168,156,114,56,72,170,270,324,336,324,270,

%U 170,72,90,242,440,594,660,660,594,440,242,90,110,332,682,1034,1254,1320,1254,1034,682,332,110

%N Triangle read by rows: left and right edges are A002378, interior entries are filled in using the Pascal triangle rule.

%e Triangle begins:

%e 0

%e 2, 2

%e 6, 4, 6

%e 12, 10, 10, 12

%e 20, 22, 20, 22, 20

%e 30, 42, 42, 42, 42, 30

%e 42, 72, 84, 84, 84, 72, 42

%e 56, 114, 156, 168, 168, 156, 114, 56

%e ...

%p d:=[seq(n*(n+1),n=0..14)];

%p f:=proc(d) local T,M,n,i;

%p M:=nops(d);

%p T:=Array(0..M-1,0..M-1);

%p for n from 0 to M-1 do T[n,0]:=d[n+1]; T[n,n]:=d[n+1]; od:

%p for n from 2 to M-1 do

%p for i from 1 to n-1 do T[n,i]:=T[n-1,i-1]+T[n-1,i]; od: od:

%p lprint("triangle:");

%p for n from 0 to M-1 do lprint(seq(T[n,i],i=0..n)); od:

%p lprint("row sums:");

%p lprint([seq( add(T[i,j],j=0..i), i=0..M-1)]);

%p end;

%p f(d);

%t 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 *)

%Y Cf. A007318, A002378, A222403, A222405.

%Y Row sums are 4*A000295.

%K nonn,tabl

%O 0,2

%A _N. J. A. Sloane_, Feb 18 2013

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Last modified January 17 09:32 EST 2020. Contains 330949 sequences. (Running on oeis4.)