A131065 - OEIS

%I #22 Sep 08 2022 08:45:30

%S 1,1,1,1,7,1,1,13,13,1,1,19,31,19,1,1,25,55,55,25,1,1,31,85,115,85,31,

%T 1,1,37,121,205,205,121,37,1,1,43,163,331,415,331,163,43,1,1,49,211,

%U 499,751,751,499,211,49,1,1,55,265,715,1255,1507,1255,715,265,55,1

%N Triangle read by rows: T(n,k) = 6*binomial(n,k) - 5 for 0 <= k <= n.

%C Row sums = A131066.

%C The matrix inverse starts:

%C        1;

%C       -1,       1;

%C        6,      -7,      1;

%C      -66,      78,    -13,      1;

%C     1086,   -1284,    216,    -19,   1;

%C   -23826,   28170,  -4740,    420, -25,   1;

%C   653406, -772536, 129990, -11520, 690, -31, 1; - _R. J. Mathar_, Mar 12 2013

%H Indranil Ghosh, <a href="/A131065/b131065.txt">Rows 0..120 of triangle, flattened</a>

%F G.f.: (1-z-t*z+6*t*z^2)/((1-z)*(1-t*z)*(1-z-t*z)). - _Emeric Deutsch_, Jun 20 2007

%e First few rows of the triangle are:

%e   1;

%e   1,  1;

%e   1,  7,  1;

%e   1, 13, 13,  1;

%e   1, 19, 31, 19,  1;

%e   1, 25, 55, 55, 25, 1;

%e ...

%p T := proc (n, k) if k <= n then 6*binomial(n, k)-5 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[6*Binomial[n,k]-5,{n,0,15},{k,0,n}]//Flatten (* _Harvey P. Dale_, May 15 2016 *)

%o (Magma) [6*Binomial(n,k) -5: k in [0..n], n in [0..10]]; // _G. C. Greubel_, Mar 12 2020

%o (Sage) [[6*binomial(n,k) -5 for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, Mar 12 2020

%Y Cf. A109128, A123203, A131060, A131061, A131063, A131064, 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