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A222405 Triangle read by rows: left and right edges are A002061 (1,3,7,13,21,...), interior entries are filled in using the Pascal triangle rule. 4
1, 3, 3, 7, 6, 7, 13, 13, 13, 13, 21, 26, 26, 26, 21, 31, 47, 52, 52, 47, 31, 43, 78, 99, 104, 99, 78, 43, 57, 121, 177, 203, 203, 177, 121, 57, 73, 178, 298, 380, 406, 380, 298, 178, 73, 91, 251, 476, 678, 786, 786, 678, 476, 251, 91, 111, 342, 727, 1154, 1464, 1572, 1464, 1154, 727, 342, 111 (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:

1

3, 3

7, 6, 7

13, 13, 13, 13

21, 26, 26, 26, 21

31, 47, 52, 52, 47, 31

43, 78, 99, 104, 99, 78, 43

57, 121, 177, 203, 203, 177, 121, 57

73, 178, 298, 380, 406, 380, 298, 178, 73

...

MAPLE

d:=[seq(n*(n+1)+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^2+n+1; t[n_, 0] := n^2+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 14 2014 *)

CROSSREFS

Cf. A007318, A002061, A222403, A222404.

Row sums are A027178.

Sequence in context: A045773 A256700 A175039 * A146970 A078708 A096273

Adjacent sequences:  A222402 A222403 A222404 * A222406 A222407 A222408

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Feb 18 2013

STATUS

approved

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Last modified October 27 01:00 EDT 2021. Contains 348270 sequences. (Running on oeis4.)