A110449 Triangle read by rows: T(n,k) = n*((2*k+1)*n+1)/2, 0<=k<=n.

0, 1, 2, 3, 7, 11, 6, 15, 24, 33, 10, 26, 42, 58, 74, 15, 40, 65, 90, 115, 140, 21, 57, 93, 129, 165, 201, 237, 28, 77, 126, 175, 224, 273, 322, 371, 36, 100, 164, 228, 292, 356, 420, 484, 548, 45, 126, 207, 288, 369, 450, 531, 612, 693, 774, 55, 155, 255, 355, 455, 555, 655, 755, 855, 955, 1055

Offset

0,3

Comments

Row sums give A110450; central terms give A110451;

T(n,0) = A000217(n);

T(n,1) = A005449(n) for n>0;

T(n,2) = A005475(n) for n>1;

T(n,3) = A022265(n) for n>2;

T(n,4) = A022267(n) for n>3;

T(n,5) = A022269(n) for n>4;

T(n,6) = A022271(n) for n>5;

T(n,7) = A022263(n) for n>6;

T(n+1,n-1) = A059270(n) for n>1;

T(n,n-1) = A081436(n) for n>1;

T(n,n) = A085786(n).

Links

G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Formula

T(n,k) = n*((2*k + 1)*n + 1)/2, 0 <= k <= n.

Example

Triangle starts:
0;
1, 2;
3, 7, 11;
6, 15, 24, 33;
10, 26, 42, 58, 74;
...

Mathematica

Table[n*((2*k + 1)*n + 1)/2, {n, 0, 10}, {k, 0, n}] // Flatten (* G. C. Greubel, Aug 23 2017 *)

Prog

(PARI) tabl(nn) = {for (n=0, nn, for (k=0, n, print1(n*((2*k+1)*n+1)/2, ", "); ); print(); ); } \\ Michel Marcus, Jun 22 2015

Crossrefs

Cf. A126890.

Sequence in context: A345742 A064956 A348745 * A229082 A176363 A067991

Adjacent sequences: A110446 A110447 A110448 * A110450 A110451 A110452

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Jul 21 2005

Status

approved