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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.)