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A174006 Array T(n, k) = k^(n-1) + (k-1)*cos(n*Pi/2), read by antidiagonals. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified July 3 10:20 EDT 2020. Contains 335417 sequences. (Running on oeis4.)