This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A205575 #22 Feb 03 2025 11:29:05
%S A205575 1,1,0,2,2,1,3,5,4,1,5,12,14,8,2,8,25,38,32,15,3,13,50,94,104,71,28,5,
%T A205575 21,96,215,293,260,149,51,8,34,180,468,756,822,612,304,92,13,55,331,
%U A205575 980,1828,2346,2136,1376,604,164,21
%N A205575 Triangle read by rows, related to Pascal's triangle, starting with rows 1; 1,0.
%C A205575 Antidiagonal sums are in A052980, row sums are in A046717.
%C A205575 Similar to A091533 and to A091562. Triangle satisfying the same recurrence as A091533 and A091562, but with the initial values T(0,0) = 1, T(0,1) = 1, T(1,1) = 0.
%F A205575 T(n,k) = T(n-1,k) + T(n-1,k-1) + T(n-2,k) + T(n-2,k-1) + T(n-2,k-2) for n>=2, k>=0, with initial conditions specified by first two rows. T(0,0) = 1, T(1,0) = 1, T(1,1) = 0.
%e A205575 Triangle begins :
%e A205575 1
%e A205575 1, 0
%e A205575 2, 2, 1
%e A205575 3, 5, 4, 1
%e A205575 5, 12, 14, 8, 2
%e A205575 8, 25, 38, 32, 15, 3
%e A205575 13, 50, 94, 104, 71, 28, 5
%o A205575 (PARI) T(n,k) = {if(n<0, return(0)); if (n==0, if (k<0, return(0)); if (k==0, return(1))); if (n==1, if (k<0, return(0)); if (k==0, return(1)); if (k==1, return(0))); T(n-1,k)+T(n-1,k-1)+T(n-2,k)+T(n-2,k-1)+T(n-2,k-2);} \\ _Michel Marcus_, Oct 27 2021
%Y A205575 Cf. Column 0: A000045, Diagonals : A000045, A029907, A036681.
%Y A205575 Cf. A090171, A090172, A090173, A090174, A091533, A091562 (same recurrence).
%K A205575 nonn,tabl
%O A205575 0,4
%A A205575 _Philippe Deléham_, Jan 29 2012
%E A205575 a(46), a(48) corrected by _Georg Fischer_, Oct 27 2021