A174006 Array T(n, k) = k^(n-1) + (k-1)*cos(n*Pi/2), read by antidiagonals.

1, 1, 1, 4, 1, 1, 9, 9, 1, 1, 16, 29, 16, 1, 1, 31, 81, 67, 25, 1, 1, 64, 241, 256, 129, 36, 1, 1, 129, 729, 1021, 625, 221, 49, 1, 1, 256, 2189, 4096, 3121, 1296, 349, 64, 1, 1, 511, 6561, 16387, 15625, 7771, 2401, 519, 81, 1, 1, 1024, 19681, 65536, 78129, 46656, 16801, 4096, 737, 100, 1, 1

Offset

2,4

Comments

Row sums are {1, 2, 6, 20, 63, 206, 728, 2776, 11373, 49858, ...}.

Links

G. C. Greubel, Antidiagonals n = 2..100, flattened

Formula

T(n, k) = k^(n-1) + (k-1)*cos(n*Pi/2).

Example

Triangle begins as:
    1;
    1,    1;
    4,    1,     1;
    9,    9,     1,     1;
   16,   29,    16,     1,    1;
   31,   81,    67,    25,    1,    1;
   64,  241,   256,   129,   36,    1,   1;
  129,  729,  1021,   625,  221,   49,   1,  1;
  256, 2189,  4096,  3121, 1296,  349,  64,  1, 1;
  511, 6561, 16387, 15625, 7771, 2401, 519, 81, 1, 1;

Maple

T(n, k):= k^(n-1) + (k-1)*cos(n*Pi/2); seq(seq(T(n-k+1, k), k=2..n), n=2..12); # G. C. Greubel, Nov 28 2019

Mathematica

T[n_, k_]:= k^(n-1) + (k-1)*Cos[n*Pi/2]; Table[T[n-k+1, k], {n, 2, 12}, {k, 2, n}]//Flatten (* modified by G. C. Greubel, Nov 28 2019 *)

Prog

(PARI) T(n, k) = round(k^(n-1) + (k-1)*cos(n*Pi/2));
for(n=2, 12, for(k=2, n, print1(T(n-k+1, k), ", "))) \\ G. C. Greubel, Nov 28 2019
(Magma)
R:= RealField(10);
function T(n, k) return Round(k^(n-1) + (k-1)*Cos(n*Pi(R)/2)); end function;
[T(n-k+1, k): k in [2..n], n in [2..12]]; // G. C. Greubel, Nov 28 2019
(Sage)
@CachedFunction
def T(n, k): return k^(n-1) + (k-1)*cos(n*pi/2)
[[T(n-k+1, k) for k in (2..n)] for n in (2..12)] # G. C. Greubel, Nov 28 2019

Crossrefs

Sequence in context: A176282 A082043 A177944 * A124216 A008459 A259333

Adjacent sequences: A174003 A174004 A174005 * A174007 A174008 A174009

Keyword

nonn,tabl

Author

Roger L. Bagula, Mar 05 2010

Extensions

Edited by G. C. Greubel, Dec 02 2019

Status

approved