# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a164899
Showing 1-1 of 1

%I A164899 #13 Feb 10 2023 05:42:39
%S A164899 1,1,10,1,11,100,1,12,110,1000,1,13,121,1100,10000,1,14,133,1210,
%T A164899 11000,100000,1,15,146,1331,12100,110000,1000000,1,16,160,1464,13310,
%U A164899 121000,1100000,10000000,1,17,175,1610,14641,133100,1210000,11000000,100000000
%N A164899 Binomial matrix (1,10^n) read by antidiagonals.
%H A164899 G. C. Greubel, <a href="/A164899/b164899.txt">Antidiagonals n = 1..50, flattened</a>
%F A164899 Sum_{k=1..n} T(n, k) = A094704(n).
%F A164899 As a triangle T(n,k) read by rows, T(n,1) = 1, T(n,n) = 10^(n-1), and T(n,k) = T(n-1, k) + T(n-2, k-1) otherwise. - _Joerg Arndt_, Dec 10 2016
%F A164899 From _G. C. Greubel_, Feb 10 2023: (Start)
%F A164899 A(n, k) = A(n-1, k) + A(n-1, k-1), with A(n, 1) = 1 and A(1, k) = 10^(k-1) (array).
%F A164899 T(n, k) = A(n-k+1, k) (antidiagonal triangle). (End)
%e A164899 Matrix array, A(n, k), begins:
%e A164899   1, 10, 100, 1000, ...
%e A164899   1, 11, 110, 1100, ...
%e A164899   1, 12, 121, 1210, ...
%e A164899   1, 13, 133, 1331, ...
%e A164899   1, 14, 146, 1464, ...
%e A164899   1, 15, 160, 1610, ...
%e A164899 Antidiagonal triangle, T(n, k), begins as:
%e A164899   1;
%e A164899   1, 10;
%e A164899   1, 11, 100;
%e A164899   1, 12, 110, 1000;
%e A164899   1, 13, 121, 1100, 10000;
%e A164899   1, 14, 133, 1210, 11000, 100000;
%e A164899   1, 15, 146, 1331, 12100, 110000, 1000000;
%t A164899 T[n_, k_]:= T[n,k]= If[k==n, 10^(n-1), If[k==1, 1, T[n-1,k] +T[n-2, k-1]]];
%t A164899 Table[T[n, k], {n,15}, {k,n}]//Flatten (* _G. C. Greubel_, Feb 10 2023 *)
%o A164899 (Magma)
%o A164899 function T(n,k) // T = A164899
%o A164899   if k eq n then return 10^(n-1);
%o A164899   elif k eq 1 then return 1;
%o A164899   else return T(n-1,k) + T(n-2,k-1);
%o A164899   end if; return T;
%o A164899 end function;
%o A164899 [T(n,k): k in [1..n], n in [1..15]]; // _G. C. Greubel_, Feb 10 2023
%o A164899 (SageMath)
%o A164899 def T(n,k): # T = A164899
%o A164899     if (k==n): return 10^(n-1)
%o A164899     elif (k==1): return 1
%o A164899     else: return T(n-1,k) + T(n-2,k-1)
%o A164899 flatten([[T(n,k) for k in range(1,n+1)] for n in range(1,16)]) # _G. C. Greubel_, Feb 10 2023
%Y A164899 Cf. A001020, A007318, A021093, A164844.
%Y A164899 Cf. A094704 (antidiagonal row sums).
%K A164899 nonn,tabl
%O A164899 1,3
%A A164899 _Mark Dols_, Aug 30 2009

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE