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A156319 Triangle by columns: (1, 2, 0, 0, 0,...) in every column. 2
1, 2, 1, 0, 2, 1, 0, 0, 2, 1, 0, 0, 0, 2, 1, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Binomial transform of the triangle = A110813.

Eigensequence of the triangle = A001045

Inverse = a triangle with (1, -2, 4, -8, 16,...) in every column.

Triangle T(n,k), 0<=k<=n, given by [2,-2,0,0,0,0,0,0,...] DELTA [1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938. -  Philippe Deléham, Feb 08 2009

LINKS

G. C. Greubel, Rows n = 1..100 of triangle, flattened

FORMULA

Triangle read by rows, T(n,k) = 1 if (n = k); 2 if k = n-1, 0 otherwise.

By columns, (1, 2, 0, 0, 0,...) in every column.

T(n,k) = A097806(n,k)*2^(n-k). - Philippe Deléham, Feb 08 2009

G.f.: (1+2*x)*x*y/(1-x*y). - R. J. Mathar, Aug 12 2015

EXAMPLE

First few rows of the triangle =

  1;

  2, 1;

  0, 2, 1;

  0, 0, 2, 1;

  0, 0, 0, 2, 1;

  0, 0, 0, 0, 2, 1;

  0, 0, 0, 0, 0, 2, 1;

  0, 0, 0, 0, 0, 0, 2, 1;

  0, 0, 0, 0, 0, 0, 0, 2, 1;

...

MAPLE

T:= proc (n) option remember;

if k=n then 1

elif k=n-1 then 2

else 0 fi;

end proc;

seq(seq(T(n, k), k=1..n), n = 1..15); # G. C. Greubel, Sep 20 2019

MATHEMATICA

Table[If[k==n, 1, If[k==n-1, 2, 0]], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Sep 20 2019 *)

PROG

(PARI) T(n, k) = if(k==n, 1, if(k==n-1, 2, 0)); \\ G. C. Greubel, Sep 20 2019

(MAGMA) T:= func< n, k | k eq n select 1 else k eq n-1 select 2 else 0 >;

[T(n, k): k in [1..n], n in [1..15]]; // G. C. Greubel, Sep 20 2019

(Sage)

def T(n, k):

    if (k==n): return 1

    elif (k==n-1): return 2

    else: return 0

[[T(n, k) for k in (1..n)] for n in (1..15)] # G. C. Greubel, Sep 20 2019

(GAP)

T:= function(n, k)

    if k=n then return 1;

    elif k=n-1 then return 2;

    else return 0;

    fi;

  end;

Flat(List([1..15], n-> List([1..n], k-> T(n, k) ))); # G. C. Greubel, Sep 20 2019

CROSSREFS

Cf. A001045, A097806, A110813.

Sequence in context: A058531 A093073 A251635 * A190893 A030204 A083650

Adjacent sequences:  A156316 A156317 A156318 * A156320 A156321 A156322

KEYWORD

nonn,tabl,easy

AUTHOR

Gary W. Adamson, Feb 07 2009

EXTENSIONS

More terms added by G. C. Greubel, Sep 20 2019

STATUS

approved

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Last modified October 23 17:32 EDT 2019. Contains 328373 sequences. (Running on oeis4.)