

A132111


Triangle read by rows: T(n,k) = n^2 + k*n + k^2, 0<=k<=n.


9



0, 1, 3, 4, 7, 12, 9, 13, 19, 27, 16, 21, 28, 37, 48, 25, 31, 39, 49, 61, 75, 36, 43, 52, 63, 76, 91, 108, 49, 57, 67, 79, 93, 109, 127, 147, 64, 73, 84, 97, 112, 129, 148, 169, 192, 81, 91, 103, 117, 133, 151, 171, 193, 217, 243, 100, 111, 124, 139, 156, 175, 196, 219
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OFFSET

0,3


COMMENTS

Permutation of A003136, the Loeschian numbers. [This is false  some terms are repeated, the first being 49  Joerg Arndt, Dec 18 2015]
Row sums give A132112.
Central terms give A033582.
T(n,k+1) = T(n,k) + n+2*k+1;
T(n+1,k) = T(n,k) + 2*n+k+1;
T(n+1,k+1) = T(n,k) + 3*(n+k+1);
T(n,0) = A000290(n);
T(n,1) = A002061(n+1) for n>0;
T(n,2) = A117950(n+1) for n>1;
T(n,n2) = A056107(n1) for n>1;
T(n,n1) = A003215(n1) for n>0;
T(n,n) = A033428(n).


LINKS

Table of n, a(n) for n=0..62.


EXAMPLE

Triangle begins:
0;
1, 3;
4, 7, 12;
9, 13, 19, 27;
16, 21, 28, 37, 48;
25, 31, 39, 49, 61, 75;
36, 43, 52, 63, 76, 91, 108;
49, 57, 67, 79, 93, 109, 127, 147;
64, 73, 84, 97, 112, 129, 148, 169, 192;
81, 91, 103, 117, 133, 151, 171, 193, 217, 243;
 Philippe Deléham, Apr 16 2014


MATHEMATICA

Flatten[Table[n^2+k*n+k^2, {n, 0, 10}, {k, 0, n}]] (* Harvey P. Dale, Jun 10 2013 *)


CROSSREFS

Sequence in context: A041153 A041781 A042893 * A164831 A085188 A286728
Adjacent sequences: A132108 A132109 A132110 * A132112 A132113 A132114


KEYWORD

nonn,tabl


AUTHOR

Reinhard Zumkeller, Aug 10 2007


STATUS

approved



