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A095195 T(n,0) = prime(n), T(n,k) = T(n,k-1)-T(n-1,k-1), 0<=k<n, triangle read by rows. 4
2, 3, 1, 5, 2, 1, 7, 2, 0, -1, 11, 4, 2, 2, 3, 13, 2, -2, -4, -6, -9, 17, 4, 2, 4, 8, 14, 23, 19, 2, -2, -4, -8, -16, -30, -53, 23, 4, 2, 4, 8, 16, 32, 62, 115, 29, 6, 2, 0, -4, -12, -28, -60, -122, -237, 31, 2, -4, -6, -6, -2, 10, 38, 98, 220, 457, 37, 6, 4, 8, 14, 20, 22, 12 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

T(n,0)=A000040(n); T(n,1)=A001223(n-1) for n>1; T(n,2)=A036263(n-2) for n>2; T(n,n-1)=A007442(n) for n>1.

LINKS

Alois P. Heinz, Rows n = 1..141, flattened

EXAMPLE

Triangle begins:

   2;

   3,  1;

   5,  2,  1;

   7,  2,  0, -1;

  11,  4,  2,  2,  3;

  13,  2, -2, -4, -6, -9;

Alternative: array form read by antidiagonals:

     2,   3,   5,   7,  11,  13,  17,  19,  23,  29,  31,...

     1,   2,   2,   4,   2,   4,   2,   4,   6,   2,   6,...

     1,   0,   2,  -2,   2,  -2,   2,   2,  -4,   4,  -2,...

    -1,   2,  -4,   4,  -4,   4,   0,  -6,   8,  -6,   0,...

     3,  -6,   8,  -8,   8,  -4,  -6,  14, -14,   6,   4,...

    -9,  14, -16,  16, -12,  -2,  20, -28,  20,  -2,  -8,...

    23, -30,  32, -28,  10,  22, -48,  48, -22,  -6,  10,..,

   -53,  62, -60,  38,  12, -70,  96, -70,  16,  16, -12,...

   115,-122,  98, -26, -82, 166,-166,  86,   0, -28,  28,...

  -237, 220,-124, -56, 248,-332, 252, -86, -28,  56, -98,...

   457,-344,  68, 304,-580, 584,-338,  58,  84,-154, 308,...

MAPLE

A095195A := proc(n, k) # array, k>=0, n>=0

    option remember;

    if n =0 then

        ithprime(k+1) ;

    else

        procname(n-1, k+1)-procname(n-1, k) ;

    end if;

end proc:

A095195 := proc(n, k) # triangle, 0<=k<n, n>=1

        A095195A(k, n-k-1) ;

end proc: # R. J. Mathar, Sep 19 2013

MATHEMATICA

T[n_, 0] := Prime[n]; T[n_, k_] /; 0 <= k < n := T[n, k] = T[n, k-1] - T[n-1, k-1]; Table[T[n, k], {n, 1, 12}, {k, 0, n-1}] // Flatten (* Jean-Fran├žois Alcover, Feb 01 2017 *)

PROG

(Haskell)

a095195 n k = a095195_tabl !! (n-1) !! (k-1)

a095195_row n = a095195_tabl !! (n-1)

a095195_tabl = f a000040_list [] where

   f (p:ps) xs = ys : f ps ys where ys = scanl (-) p xs

-- Reinhard Zumkeller, Oct 10 2013

CROSSREFS

Cf. A036262-A036271.

Cf. A140119 (row sums).

Sequence in context: A173239 A214055 A066909 * A229961 A189074 A255973

Adjacent sequences:  A095192 A095193 A095194 * A095196 A095197 A095198

KEYWORD

sign,tabl,look

AUTHOR

Reinhard Zumkeller, Jun 22 2004

STATUS

approved

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Last modified June 21 13:06 EDT 2021. Contains 345364 sequences. (Running on oeis4.)