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
Triangle T(n,k) (with rows n >= 0 and columns k = 0..n) begins:
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
KEYWORD
AUTHOR
Gary W. Adamson, Jun 15 2007
EXTENSIONS
Corrected and extended by Emeric Deutsch, Jun 20 2007
STATUS
approved