A131063 - OEIS

%I #19 Sep 08 2022 08:45:30

%S 1,1,1,1,6,1,1,11,11,1,1,16,26,16,1,1,21,46,46,21,1,1,26,71,96,71,26,

%T 1,1,31,101,171,171,101,31,1,1,36,136,276,346,276,136,36,1,1,41,176,

%U 416,626,626,416,176,41,1,1,46,221,596,1046,1256,1046,596,221,46,1

%N Triangle read by rows: T(n,k) = 5*binomial(n,k) - 4  for 0 <= k <= n.

%C Row sums = A131064: (1, 2, 8, 24, 60, 136, 292, ...), the binomial transform of (1, 1, 5, 5, 5, ...).

%H Muniru A Asiru, <a href="/A131063/b131063.txt">Rows n=0..100 of triangle, flattened</a>

%F G.f.: (1-z-t*z+5*t*z^2)/((1-z)*(1-t*z)*(1-z-t*z)). - _Emeric Deutsch_, Jun 20 2007

%e First few rows of the triangle:

%e   1;

%e   1,  1;

%e   1,  6,  1;

%e   1, 11, 11,  1;

%e   1, 16, 26, 16,  1;

%e   1, 21, 46, 46, 21,  1;

%e   1, 26, 71, 96, 71, 26,  1;

%e   ...

%p T := proc (n, k) if k <= n then 5*binomial(n, k)-4 else 0 end if end proc: for n from 0 to 10 do seq(T(n, k), k = 0 .. n) end do; # _Emeric Deutsch_, Jun 20 2007

%t Table[5*Binomial[n,k] -4, {n,0,10}, {k,0,n}]//Flatten (* _G. C. Greubel_, Mar 12 2020 *)

%o (GAP) Print(Flat(List([0..10],n->List([0..n],k->5*Binomial(n,k)-4)))); # _Muniru A Asiru_, Feb 21 2019

%o (Magma) [5*Binomial(n, k) -4: k in [0..n], n in [0..10]]; // _G. C. Greubel_, Mar 12 2020

%o (Sage) [[5*binomial(n, k) -4 for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, Mar 12 2020

%Y Cf. A109128, A123203, A131060, A131061, A131064, A131065, A131066, A131067, A131068.

%K nonn,tabl

%O 0,5

%A _Gary W. Adamson_, Jun 13 2007

%E More terms from _Emeric Deutsch_, Jun 20 2007