cp's OEIS Frontend

A207260 Triangle read by rows: T(n,k) = k^2 + (1-(-1)^(n-k))/2.

%I A207260 #47 Nov 13 2024 16:31:03
%S A207260 0,1,1,0,2,4,1,1,5,9,0,2,4,10,16,1,1,5,9,17,25,0,2,4,10,16,26,36,1,1,
%T A207260 5,9,17,25,37,49,0,2,4,10,16,26,36,50,64,1,1,5,9,17,25,37,49,65,81,0,
%U A207260 2,4,10,16,26,36,50,64,82,100,1,1,5,9,17,25,37,49,65,81,101,121
%N A207260 Triangle read by rows: T(n,k) = k^2 + (1-(-1)^(n-k))/2.
%C A207260 Row sums are A171218(n).
%H A207260 Paolo Xausa, <a href="/A207260/b207260.txt">Table of n, a(n) for n = 0..11475</a> (rows 0..150 of triangle, flattened).
%F A207260 T(n+k, n) = A002522(n) if k is odd.
%F A207260 T(n+k, n) = n^2 = A000290(n) if k is even.
%F A207260 T(2*n, n) = A137928(n), n>0.
%F A207260 T(2*n+1, n+1) = A080335(n).
%F A207260 T(n,0) = A000035(n).
%F A207260 T(n+1,1) = A000034(n).
%F A207260 T(n+2,2) = A010710(n).
%F A207260 T(n+3,3) = A010735(n).
%F A207260 Sum_{k, 0<=k<=n} T(n,k)*x^k = (-1)^n*A007590(n), A000035(n), A171218(n)
%F A207260 for x = -1, 0, 1 respectively.
%F A207260 G.f.: x*(1 + y - x*y + x*(1 + 2*x)*y^2)/((1 - x^2)*(1 - x*y)^3). - _Stefano Spezia_, Nov 12 2024
%e A207260 Triangle begins:
%e A207260   0;
%e A207260   1, 1;
%e A207260   0, 2, 4;
%e A207260   1, 1, 5,  9;
%e A207260   0, 2, 4, 10, 16;
%e A207260   1, 1, 5,  9, 17, 25;
%e A207260   0, 2, 4, 10, 16, 26, 36;
%e A207260   1, 1, 5,  9, 17, 25, 37, 49;
%e A207260   0, 2, 4, 10, 16, 26, 36, 50, 64;
%e A207260   1, 1, 5,  9, 17, 25, 37, 49, 65, 81;
%e A207260   ...
%t A207260 Table[k^2 + (1-(-1)^(n-k))/2, {n, 0, 15}, {k, 0, n}] (* _Paolo Xausa_, Nov 13 2024 *)
%o A207260 (Magma) /* As triangle */ [[ k^2 + (1-(-1)^(n-k))/2: k in [0..n]]: n in [0.. 15]]; // _Vincenzo Librandi_, Nov 09 2024
%Y A207260 Cf. A000034, A000035, A000290, A002522, A007590, A010710, A010735, A080335, A171218, A137928.
%K A207260 easy,nonn,tabl
%O A207260 0,5
%A A207260 _Philippe Deléham_, Feb 16 2012