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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

Table of n, a(n) for n=0..65.

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-Fran├žois 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 October 15 18:04 EDT 2021. Contains 348033 sequences. (Running on oeis4.)