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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 (list; table; graph; refs; listen; history; text; internal format)
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,n-2) = A056107(n-1) for n>1;

T(n,n-1) = A003215(n-1) 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

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Last modified September 20 16:14 EDT 2017. Contains 292276 sequences.