login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A131115 Triangle read by rows: T(n,k) = 7*binomial(n,k) with T(n,n)=1. 7
1, 7, 1, 7, 14, 1, 7, 21, 21, 1, 7, 28, 42, 28, 1, 7, 35, 70, 70, 35, 1, 7, 42, 105, 140, 105, 42, 1, 7, 49, 147, 245, 245, 147, 49, 1, 7, 56, 196, 392, 490, 392, 196, 56, 1, 7, 63, 252, 588, 882, 882, 588, 252, 63, 1, 7, 70, 315, 840, 1470, 1764, 1470, 840, 315, 70, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums give A048489.

Non-diagonal entries of Pascal's triangle are multiplied by 7. - Emeric Deutsch, Jun 20 2007

The matrix inverse starts

            1;

           -7,         1;

           91,       -14,         1;

        -1771,       273,       -21,       1;

        45955,     -7084,       546,     -28,      1;

     -1490587,    229775,    -17710,     910,    -35,    1;

     58018051,  -8943522,    689325,  -35420,   1365,  -42,   1;

  -2634606331, 406126357, -31302327, 1608425, -61985, 1911, -49, 1;

- R. J. Mathar, Mar 15 2013

LINKS

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

FORMULA

G.f.: (1 + 6*x - t*x)/((1-t*x)*(1-x-t*x)). - Emeric Deutsch, Jun 20 2007

EXAMPLE

First few rows of the triangle are:

  1;

  7,  1;

  7, 14,  1;

  7, 21, 21,  1;

  7, 28, 42, 28,  1;

  7, 35, 70, 70, 35, 1;

...

MAPLE

T := proc (n, k) if k < n then 7*binomial(n, k) elif k = n then 1 else 0 end if end proc; for n from 0 to 10 do seq(T(n, k), k = 0 .. n) end do; # yields sequence in triangular form - Emeric Deutsch, Jun 20 2007

MATHEMATICA

Table[If[k==n, 1, 7*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, 7*binomial(n, k)) \\ Charles R Greathouse IV, Jan 16 2012

(MAGMA) [k eq n select 1 else 7*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 7*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 7*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, A048489, A131110, A131111, A131112, A131113, A131114.

Sequence in context: A093564 A081776 A256255 * A151778 A138616 A021937

Adjacent sequences:  A131112 A131113 A131114 * A131116 A131117 A131118

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Jun 15 2007

EXTENSIONS

Corrected and extended by Emeric Deutsch, Jun 20 2007

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 25 19:09 EST 2020. Contains 331249 sequences. (Running on oeis4.)