A123002 Triangle read by rows: T(n, k) = 2^(n-1)*(2*k - 1) - 2^(k-1)*(2*n - 1).

0, -1, 0, -1, 2, 0, 1, 10, 12, 0, 7, 30, 44, 40, 0, 21, 74, 116, 136, 112, 0, 51, 166, 268, 344, 368, 288, 0, 113, 354, 580, 776, 912, 928, 704, 0, 239, 734, 1212, 1656, 2032, 2272, 2240, 1664, 0, 493, 1498, 2484, 3432, 4304, 5024, 5440, 5248, 3840, 0

Offset

1,5

Links

G. C. Greubel, Rows n = 1..50 of the triangle, flattened

Formula

T(n, k) = 2^(n-1)*(2*k - 1) - 2^(k-1)*(2*n - 1).

Sum_{k=1..n} T(n, k) = 2^(n-1)*(n^2 - 4*n + 2) + (2*n - 1). - G. C. Greubel, Jul 14 2021

Example

Triangle begins as:
   0;
  -1,  0;
  -1,  2,   0;
   1, 10,  12,   0;
   7, 30,  44,  40,   0;
  21, 74, 116, 136, 112, 0;

Mathematica

T[n_, k_]:= 2^(n-1)*(2*k-1) -2^(k-1)*(2*n-1);
Table[T[n, k], {n, 12}, {k, n}]//Flatten

Prog

(Magma) [2^(n-1)*(2*k-1) -2^(k-1)*(2*n-1): k in [1..n], n in [1..12]]; // G. C. Greubel, Jul 14 2021
(Sage) flatten([[2^(n-1)*(2*k-1) -2^(k-1)*(2*n-1) for k in (1..n)] for n in (1..12)]) # G. C. Greubel, Jul 14 2021

Crossrefs

Sequence in context: A185410 A264676 A091803 * A261161 A361951 A137514

Adjacent sequences: A122999 A123000 A123001 * A123003 A123004 A123005

Keyword

sign,tabl

Author

Roger L. Bagula, Sep 23 2006

Extensions

Edited by N. J. A. Sloane, Oct 01 2006

Status

approved