# Python code for A372646 - John Rascoe 5/13/2024
from collections import Counter
from math import isqrt

def addp(x):
    z = []
    z.append(x+(x[-1]+1,))
    z.append((x[0]+1,)+x)
    if x[-1] > 1:
        z.append(x+(x[-1]-1,))
    if x[0] > 1:
        z.append((x[0]-1,)+x)
    return(z)

def A372646_rowlist(row_max):
    S = {(1,)}
    s = [[(1,)]]
    P = [[0],[0,1]]
    Pt = []
    #Builds triangle with rows and columns inverted first
    for i in range(row_max+1):
        C = Counter()
        s.append([])
        P.append([])
        for j in s[i]:
            for k in addp(j):
                if k not in S and sum(k) <= row_max:
                    C.update({sum(k)})
                    S.add(k)
                    s[i+1].append(k)         
        for n in range((((i+2)*(i+3))//2)+1):
            P[i+2].append(C[n])
    #inverting triangle and truncating leading 0's
    for n in range(row_max+1):
        Pt.append([])
        for k in range( ((isqrt(8*(n+1))+1)//2)-1 , (2*(n+2))//3 ):
            if n <= len(P[k])-1:
                Pt[n].append(P[k][n])
            else:
                Pt[n].append(0)
    for i in range(len(Pt)):
        print(Pt[i])

A372646_rowlist(12)