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 A169950 #22 Jun 09 2016 03:28:43
%S A169950 1,1,1,1,2,1,1,5,1,1,1,8,4,2,1,1,13,8,8,1,1,1,20,15,18,7,2,1,1,33,23,
%T A169950 45,13,11,1,1,1,48,44,86,36,28,10,2,1,1,75,64,184,70,84,18,14,1,1,1,
%U A169950 100,117,332,166,188,68,36,13,2,1,1,145,173,657,282,482,134,132,23,17,1,1
%N A169950 Consider the 2^n monic polynomials f(x) with coefficients 0 or 1 and degree n. Sequence gives triangle read by rows, in which T(n,k) (n>=0) is the number of such polynomials of thickness k (1 <= k <= n+1).
%C A169950 The thickness of a polynomial f(x) is the magnitude of the largest coefficient in the expansion of f(x)^2.
%H A169950 Gheorghe Coserea, <a href="/A169950/b169950.txt">Rows n = 0..33, flattened</a>
%H A169950 <a href="/index/Ca#CARRYLESS">Index entries for sequences related to carryless arithmetic</a>
%F A169950 Wanted: a recurrence. Are any of A169940-A169954 related to any other entries in the OEIS?
%e A169950 Triangle begins:
%e A169950 n\k [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
%e A169950 [0] 1;
%e A169950 [1] 1, 1;
%e A169950 [2] 1, 2, 1;
%e A169950 [3] 1, 5, 1, 1;
%e A169950 [4] 1, 8, 4, 2, 1;
%e A169950 [5] 1, 13, 8, 8, 1, 1;
%e A169950 [6] 1, 20, 15, 18, 7, 2, 1;
%e A169950 [7] 1, 33, 23, 45, 13, 11, 1, 1;
%e A169950 [8] 1, 48, 44, 86, 36, 28, 10, 2, 1;
%e A169950 [9] 1, 75, 64, 184, 70, 84, 18, 14, 1, 1;
%e A169950 [10] 1, 100, 117, 332, 166, 188, 68, 36, 13, 2, 1;
%e A169950 [11] 1, 145, 173, 657, 282, 482, 134, 132, 23, 17, 1, 1;
%e A169950 [12] ...
%e A169950 For n = 3, the eight polynomials, their squares and thicknesses are as follows:
%e A169950 x^3, x^6, 1
%e A169950 x^3+1, x^6+2*x^3+1, 2
%e A169950 x^3+x, x^6+2*x^4+x^2, 2
%e A169950 x^3+x+1, x^6+2*x^4+2*x^3+x^2+2*x+1, 2
%e A169950 x^3+x^2, x^6+2*x^5+x^4, 2
%e A169950 x^3+x^2+1, x^6+2*x^5+2*x^3+x^4+2*x^2+1, 2
%e A169950 x^3+x^2+x, x^6+2*x^5+3*x^4+2*x^3+x^2, 3
%e A169950 x^3+x^2+x+1, x^6+2*x^5+3*x^4+4*x^3+3*x^2+2*x+1, 4
%e A169950 Hence T(3,1) = 1, T(3,2) = 5, T(3,3) = 1, T(3,4) = 1.
%t A169950 Last /@ Tally@ # & /@ Table[Max@ CoefficientList[SeriesData[x, 0, #, 0, 2^n, 1]^2, x] &@ IntegerDigits[#, 2] & /@ Range[2^n, 2^(n + 1) - 1], {n, 12}] // Flatten (* _Michael De Vlieger_, Jun 08 2016 *)
%o A169950 (PARI)
%o A169950 seq(n) = {
%o A169950 my(a = vector(n+1, k, vector(k)), x='x);
%o A169950 for(k = 1, 2^(n+1)-1, my(pol = Pol(binary(k), x));
%o A169950 a[poldegree(pol)+1][vecmax(Vec(sqr(pol)))]++);
%o A169950 return(a);
%o A169950 };
%o A169950 concat(seq(11)) \\ _Gheorghe Coserea_, Jun 06 2016
%Y A169950 Related to thickness: A169940-A169954, A061909, A274036.
%K A169950 nonn,tabl
%O A169950 0,5
%A A169950 _N. J. A. Sloane_, Aug 01 2010
%E A169950 Rows 17-30 of the triangle from _Nathaniel Johnston_, Nov 15 2010