C1 recurrence (5) == combinatorial e_{n,i}, n<=9: PASS 
   rows 1..7: [[1], [0, 1], [1, 1, 0], [0, 1, 2, 2], [5, 5, 4, 2, 0], [0, 5, 10, 14, 16, 16], [61, 61, 56, 46, 32, 16, 0]]
   E_0..E_12 = [1, 1, 1, 2, 5, 16, 61, 272, 1385, 7936, 50521, 353792, 2702765]
C2 row sums of (5) == E_n from sec+tan, n<=400: PASS 
C3 T_{2j-1} Bernoulli formula (j<=200) and v2(T_{2j-1})=h(j) (j<=600): PASS 
C4 Lemma v2(e_(n,i)) >= G(i), all 1<=i<=n<=1200: PASS []
C5 v2(e_(2j,2j)) = h(j), 2j<=1200: PASS 
C4r refined lemma v2(e_(n,i)) >= H(i,n)=min{h(j): ceil(i/2)<=j<=floor(n/2)}, 2<=n<=1200: PASS 
C5w witness: v2(e_(2j*,i)) = G(i) with j* = least minimiser of h on [ceil(i/2),oo), all i>=3 with 2j*<=1200 (1198 columns): PASS 
C6a u_k (from triangle) == Table 1 of source, k<=18: PASS [2, 4, 4, 4, 8, 8, 8, 8, 10, 12, 12, 16, 16, 16, 16, 16, 18, 20]
C6b u_k (from triangle, rows<=1200) == F(k) for k<=1200: PASS 
C7a examples (8),(9) of the source reproduced: PASS 
C7b f-transform of (2,4,4,4) == F(k) for k<=1048576: PASS 
C7c Fvec == naive F for k<=3000: PASS 
C7d at stage a (d=2^a), x_d=2^a and cut s=2^a-a-1, for 2<=a<=19: PASS 
C8 block identities/ranges of h, 2<=a<=24 (ranges a<=20): PASS 
C9 (diagnostic) m_i(rows<=1200) == G(i) for i<=600: yes; m_i weakly increasing for i<=600: True
   m_1..m_40 = [0, 0, 1, 1, 4, 4, 4, 4, 8, 8, 9, 9, 11, 11, 11, 11, 16, 16, 17, 17, 20, 20, 20, 20, 24, 24, 25, 25, 26, 26, 26, 26, 32, 32, 33, 33, 36, 36, 36, 36]
   G_1..G_40 = [0, 0, 1, 1, 4, 4, 4, 4, 8, 8, 9, 9, 11, 11, 11, 11, 16, 16, 17, 17, 20, 20, 20, 20, 24, 24, 25, 25, 26, 26, 26, 26, 32, 32, 33, 33, 36, 36, 36, 36]
   first row attaining m_i, i=1..40: [1, 2, 4, 4, 6, 6, 8, 8, 10, 10, 12, 12, 16, 16, 16, 16, 18, 18, 20, 20, 22, 22, 24, 24, 26, 26, 28, 28, 32, 32, 32, 32, 34, 34, 36, 36, 38, 38, 40, 40]
   F(1..40) = [2, 4, 4, 4, 8, 8, 8, 8, 10, 12, 12, 16, 16, 16, 16, 16, 18, 20, 20, 20, 24, 24, 24, 24, 26, 28, 32, 32, 32, 32, 32, 32, 34, 36, 36, 36, 40, 40, 40, 40]
ALL CHECKS PASS
real 31.08
user 23.52
sys 0.19
