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A131114 T(n,k) = 6*binomial(n,k) - 5*I, where I is the identity matrix. 5
1, 6, 1, 6, 12, 1, 6, 18, 18, 1, 6, 24, 36, 24, 1, 6, 30, 60, 60, 30, 1, 6, 36, 90, 120, 90, 36, 1, 6, 42, 126, 210, 210, 126, 42, 1, 6, 48, 168, 336, 420, 336, 168, 48, 1, 6, 54, 216, 504, 756, 756, 504, 216, 54, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums give A048489.

LINKS

G. C. Greubel, Rows n = 0..100 of triangle, flattened

FORMULA

T(n,k) = 6*A007318(n,k) - 5*I, A007318 = Pascal's triangle, I = Identity matrix.

EXAMPLE

First few rows of the triangle are:

  1;

  6,  1;

  6, 12,  1;

  6, 18, 18,   1;

  6, 24, 36,  24,  1;

  6, 30, 60,  60, 30,  1;

  6, 36, 90, 120, 90, 36, 1;

...

MAPLE

seq(seq(`if`(k=n, 1, 6*binomial(n, k)), k=0..n), n=0..10); # G. C. Greubel, Nov 18 2019

MATHEMATICA

Table[If[k==n, 1, 6*Binomial[n, k]], {n, 0, 10}, {k, 0, n}]//Flatten (* G. C. Greubel, Nov 18 2019 *)

PROG

(PARI) T(n, k) = if(k==n, 1, 6*binomial(n, k)); # G. C. Greubel, Nov 18 2019

(MAGMA) [k eq n select 1 else 6*Binomial(n, k): k in [0..n], n in [0..10]]; // G. C. Greubel, Nov 18 2019

(Sage)

@CachedFunction

def T(n, k):

    if (k==n): return 1

    else: return 6*binomial(n, k)

[[T(n, k) for k in (0..n)] for n in (0..10)] # G. C. Greubel, Nov 18 2019

(GAP)

T:= function(n, k)

    if k=n then return 1;

    else return 6*Binomial(n, k);

    fi;  end;

Flat(List([0..10], n-> List([0..n], k-> T(n, k) ))); # G. C. Greubel, Nov 18 2019

CROSSREFS

Cf. A007318, A048488, A131110, A131111, A131112, A131113, A131115.

Sequence in context: A272055 A157292 A159828 * A199230 A199101 A127778

Adjacent sequences:  A131111 A131112 A131113 * A131115 A131116 A131117

KEYWORD

nonn,tabl,easy

AUTHOR

Gary W. Adamson, Jun 15 2007

STATUS

approved

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Last modified January 19 04:09 EST 2020. Contains 331031 sequences. (Running on oeis4.)