A281334 Triangle read by rows: T(n, k) = (n - k)*(k + 1)^3 + k, 0 <= k <= n.

0, 1, 1, 2, 9, 2, 3, 17, 29, 3, 4, 25, 56, 67, 4, 5, 33, 83, 131, 129, 5, 6, 41, 110, 195, 254, 221, 6, 7, 49, 137, 259, 379, 437, 349, 7, 8, 57, 164, 323, 504, 653, 692, 519, 8, 9, 65, 191, 387, 629, 869, 1035, 1031, 737, 9, 10, 73, 218, 451, 754, 1085, 1378, 1543, 1466, 1009, 10

Offset

1,4

Links

Table of n, a(n) for n=1..66.

Formula

Row sums sum_{k>=0} T(n,k) = n*(n+1)*(3*n^3+12*n^2+13*n+32)/60. - R. J. Mathar, Mar 19 2017

Example

Triangle begins:
   0;
   1,    1;
   2,    9,    2;
   3,   17,   29,    3;
   4,   25,   56,   67,    4;
   5,   33,   83,  131,  129,    5;
   6,   41,  110,  195,  254,  221,    6;
   7,   49,  137,  259,  379,  437,  349,    7;
   8,   57,  164,  323,  504,  653,  692,  519,    8;
   9,   65,  191,  387,  629,  869, 1035, 1031,  737,    9;
  10,   73,  218,  451,  754, 1085, 1378, 1543, 1466, 1009,   10;
  ...

Mathematica

t[n_, k_] := (n - k)*(k + 1)^3 + k; Table[ t[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Robert G. Wilson v, Feb 09 2017 *)

Prog

(Magma) /* As triangle */ [[(n-k)*(k+1)^3+k: k in [1..n]]: n in [0..10]];
(PARI) for(n=0, 10, for(k=0, n, print1((n-k)*(k+1)^3+k, ", "))) \\ Derek Orr, Feb 26 2017

Crossrefs

Cf. Triangle read by rows: T(n,k) = (n-k)*(k+1)^m+k: A003056 (m = 0), A059036 (m = 1), A274602 (m = 2), this sequence (m = 3).

Cf. A001477 (column 0), A017077 (column 1), A281546 (column 2), A242604 (middle diagonal).

Sequence in context: A121602 A011324 A021346 * A010597 A245253 A376911

Adjacent sequences: A281331 A281332 A281333 * A281335 A281336 A281337

Keyword

nonn,tabl,easy

Author

Juri-Stepan Gerasimov, Jan 23 2017

Status

approved