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A176339 Triangle T(n,k) = 1 - A176337(k) - A176337(n-k) + A176337(n) read by rows. 5
1, 1, 1, 1, -3, 1, 1, 17, 17, 1, 1, -239, -219, -239, 1, 1, 7169, 6933, 6933, 7169, 1, 1, -444479, -437307, -437563, -437307, -444479, 1, 1, 56004353, 55559877, 55567029, 55567029, 55559877, 56004353, 1, 1, -14225105663, -14169101307, -14169545803, -14169538395, -14169545803, -14169101307, -14225105663, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are {1, 2, -1, 36, -695, 28206, -2201133, 334262520, -99297043939, 57953303599938, -66678973493759897, ...}.

LINKS

G. C. Greubel, Rows n = 0..25 of triangle, flattened

FORMULA

T(n,k) = T(n,n-k).

EXAMPLE

Triangle begins as:

  1;

  1,       1;

  1,      -3,       1;

  1,      17,      17,       1;

  1,    -239,    -219,    -239,       1;

  1,    7169,    6933,    6933,    7169,       1;

  1, -444479, -437307, -437563, -437307, -444479, 1;

MAPLE

A176339 := proc(n, m)

    1-A176337(m)-A176337(n-m)+A176337(n) ;

end proc: # R. J. Mathar, May 04 2013

MATHEMATICA

b[n_, q_]:= b[n, q]= If[n==0, 0, (1-q^n)*b[n-1, q] +1];

T[n_, k_, q_]:= 1 + b[n, q] -b[n-k, q] - b[k, q];

Table[T[n, k, 2], {n, 0, 10}, {k, 0, n}]//Flatten (* modified by G. C. Greubel, Dec 07 2019 *)

PROG

(PARI) b(n, q) = if(n==0, 0, 1 + (1-q^n)*b(n-1, q) );

T(n, k, q) = 1 + b(n, q) - b(n-k, q) - b(k, q);

for(n=0, 10, for(k=0, n, print1(T(n, k, 2), ", "))) \\ G. C. Greubel, Dec 07 2019

(MAGMA) function b(n, q)

  if n eq 0 then return 0;

  else return 1 - (q^n-1)*b(n-1, q);

  end if; return b; end function;

function T(n, k, q) return 1 + b(n, q) - b(n-k, q) - b(k, q); end function;

[ T(n, k, 2) : k in [0..n], n in [0..10]]; // G. C. Greubel, Dec 07 2019

(Sage)

@CachedFunction

def b(n, q):

    if (n==0): return 0

    else: return 1 - (q^n-1)*b(n-1, q)

def T(n, k, q): return 1 + b(n, q) - b(n-k, q) - b(k, q)

[[T(n, k, 2) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Dec 07 2019

(GAP)

b:= function(n, q)

    if n=0 then return 0;

    else return 1 - (q^n-1)*b(n-1, q);

    fi; end;

T:= function(n, k, q) return 1 + b(n, q) - b(n-k, q) - b(k, q); end;

Flat(List([0..10], n-> List([0..n], k-> T(n, k, 2) ))); # G. C. Greubel, Dec 07 2019

CROSSREFS

Cf. A176337, A176338, A176340.

Sequence in context: A322790 A333560 A176293 * A121412 A212855 A016561

Adjacent sequences:  A176336 A176337 A176338 * A176340 A176341 A176342

KEYWORD

sign,tabl

AUTHOR

Roger L. Bagula, Apr 15 2010

STATUS

approved

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Last modified August 8 04:32 EDT 2020. Contains 336290 sequences. (Running on oeis4.)