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A135223 Triangle A000012 * A127648 * A103451, read by rows. 2
1, 3, 2, 6, 2, 3, 10, 2, 3, 4, 15, 2, 3, 4, 5, 21, 2, 3, 4, 5, 6, 28, 2, 3, 4, 5, 6, 7, 36, 2, 3, 4, 5, 6, 7, 8, 45, 2, 3, 4, 5, 6, 7, 8, 9, 55, 2, 3, 4, 5, 6, 7, 8, 9, 10, 66, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 78, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 91, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums = A028387.

LINKS

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

FORMULA

T(n,k) = A000012(n,k) * A127648(n,k) * A103451(n,k) as infinite lower triangular matrices. Replace left border of 1's in A002260 with (1, 3, 6, 10, 15,...).

T(n, k) = k with T(n,1) = binomial(n+1, 2). - G. C. Greubel, Nov 20 2019

EXAMPLE

First few rows of the triangle are:

   1;

   3, 2;

   6, 2, 3;

  10, 2, 3, 4;

  15, 2, 3, 4, 5;

...

MAPLE

seq(seq( `if`(k=1, binomial(n+1, 2), k), k=1..n), n=1..15); # G. C. Greubel, Nov 20 2019

MATHEMATICA

T[n_, k_]:= T[n, k]= If[k==1, Binomial[n+1, 2], k]; Table[T[n, k], {n, 15}, {k, n}]//Flatten (* G. C. Greubel, Nov 20 2019 *)

PROG

(PARI) T(n, k) = if(k==1, binomial(n+1, 2), k); \\ G. C. Greubel, Nov 20 2019

(MAGMA) [k eq 1 select Binomial(n+1, 2) else k: k in [1..n], n in [1..15]]; // G. C. Greubel, Nov 20 2019

(Sage)

@CachedFunction

def T(n, k):

    if (k==1): return binomial(n+1, 2)

    else: return k

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

(GAP)

T:= function(n, k)

    if k=1 then return Binomial(n+1, 2);

    else return k;

    fi; end;

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

CROSSREFS

Cf. A002260, A103451, A127648.

Sequence in context: A188614 A290798 A133519 * A143310 A131897 A061187

Adjacent sequences:  A135220 A135221 A135222 * A135224 A135225 A135226

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Nov 23 2007

EXTENSIONS

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

STATUS

approved

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Last modified April 22 07:26 EDT 2021. Contains 343163 sequences. (Running on oeis4.)