cp's OEIS Frontend

A118413 Triangle read by rows: T(n,k) = (2*n-1)*2^(k-1), 0

%I A118413 #20 Jun 21 2025 11:16:08
%S A118413 1,3,6,5,10,20,7,14,28,56,9,18,36,72,144,11,22,44,88,176,352,13,26,52,
%T A118413 104,208,416,832,15,30,60,120,240,480,960,1920,17,34,68,136,272,544,
%U A118413 1088,2176,4352,19,38,76,152,304,608,1216,2432,4864,9728,21,42,84,168
%N A118413 Triangle read by rows: T(n,k) = (2*n-1)*2^(k-1), 0<k<=n.
%C A118413 Central terms give A118415; row sums give A118414;
%C A118413 T(n,1) = A005408(n-1);
%C A118413 T(n,2) = A016825(n-1) for n>1;
%C A118413 T(n,3) = A017113(n-1) for n>2;
%C A118413 T(n,4) = A051062(n-1) for n>3;
%C A118413 T(n,n-2) = A052951(n-1) for n>2;
%C A118413 T(n,n) = A014480(n-1) = A118416(n,n);
%C A118413 A001511(T(n,k)) = A002260(n,k);
%C A118413 A003602(T(n,k)) = A002024(n,k).
%C A118413 G.f.: x*y*(1 + x + 2*x*y - 6*x^2*y)/((1 - x)^2*(1 - 2*x*y)^2). - _Stefano Spezia_, Dec 22 2024
%e A118413    1
%e A118413    3   6
%e A118413    5  10  20
%e A118413    7  14  28  56
%e A118413    9  18  36  72 144
%e A118413   11  22  44  88 176 352
%e A118413   13  26  52 104 208 416  832
%e A118413   15  30  60 120 240 480  960 1920
%e A118413   17  34  68 136 272 544 1088 2176 4352
%e A118413   19  38  76 152 304 608 1216 2432 4864 9728
%e A118413   ...
%t A118413 Select[Flatten[Table[(2n-1)2^(k-1),{n,20},{k,0,n}]],IntegerQ] (* _Harvey P. Dale_, Jan 17 2024 *)
%o A118413 (Python)
%o A118413 from math import isqrt, comb
%o A118413 def A118413(n):
%o A118413     a = (m:=isqrt(k:=n<<1))+(k>m*(m+1))
%o A118413     return ((a<<1)-1)<<n-comb(a,2)-1 # _Chai Wah Wu_, Jun 20 2025
%Y A118413 Cf. A001511, A002024, A002260, A003602, A005408, A014480, A016825, A017113, A051062, A052951, A117303, A118414, A118415, A118416, A117303.
%K A118413 nonn,tabl,easy
%O A118413 1,2
%A A118413 _Reinhard Zumkeller_, Apr 27 2006