login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A176340 Triangle T(n,k) = 1 - A176338(k) - A1763378(n-k) + A176338(n) read by rows. 2
1, 1, 1, 1, -8, 1, 1, 190, 190, 1, 1, -14822, -14624, -14822, 1, 1, 3557278, 3542464, 3542464, 3557278, 1, 1, -2582583830, -2579026544, -2579041556, -2579026544, -2582583830, 1, 1, 5640363084718, 5637780500896, 5637784057984, 5637784057984, 5637780500896, 5640363084718, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Row sums are: {1, 2, -6, 382, -44266, 14199486, -12902262302, 33831855287198,

-258898313695820850, 5823405140242006622494, -386839522966544578870468774, ...}.

LINKS

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

FORMULA

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

EXAMPLE

Triangle starts as:

  1;

  1,       1;

  1,      -8,       1;

  1,     190,     190,       1;

  1,  -14822,  -14624,  -14822,       1;

  1, 3557278, 3542464, 3542464, 3557278, 1;

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, 3], {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, 3), ", "))) \\ 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, 3) : 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, 3) 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, 3) ))); # G. C. Greubel, Dec 07 2019

CROSSREFS

Cf. A176337, A176338, A176339.

Sequence in context: A015121 A156766 A178046 * A111835 A254460 A198830

Adjacent sequences:  A176337 A176338 A176339 * A176341 A176342 A176343

KEYWORD

sign,tabl

AUTHOR

Roger L. Bagula, Apr 15 2010

EXTENSIONS

Edited by G. C. Greubel, Dec 07 2019

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 11 23:45 EDT 2020. Contains 336434 sequences. (Running on oeis4.)