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Empirical: a(n) = -a(n-1) -a(n-2) +a(n-3) +a(n-4) +2*a(n-5) +a(n-6) +a(n-7) -a(n-8) -a(n-9) -a(n-10) +a(n-12) +a(n-13) +a(n-14) -a(n-15) -a(n-16) -2*a(n-17) -a(n-18) -a(n-19) +a(n-20) +a(n-21) +a(n-22) for n>36.
Also empirically a quasipolynomial of degree 2 with period 60, the first 12 being (empirical formulas for n>14):
for n mod 60 = 0: a(n) = (307/3)*n^2 + (175303/30)*n + 53785;
for n mod 60 = 1: a(n) = (3107/24)*n^2 + (109097/20)*n + (6308123/120);
for n mod 60 = 2: a(n) = (10769/72)*n^2 + (977923/180)*n + (2138171/45);
for n mod 60 = 3: a(n) = (307/3)*n^2 + (175303/30)*n + (523367/10);
for n mod 60 = 4: a(n) = (3107/24)*n^2 + (109097/20)*n + (815764/15);
for n mod 60 = 5: a(n) = (10769/72)*n^2 + (977923/180)*n + (3756257/72);
for n mod 60 = 6: a(n) = (307/3)*n^2 + (175303/30)*n + (289877/5);
for n mod 60 = 7: a(n) = (3107/24)*n^2 + (109097/20)*n + (5353751/120);
for n mod 60 = 8: a(n) = (10769/72)*n^2 + (977923/180)*n + (2363234/45);
for n mod 60 = 9: a(n) = (307/3)*n^2 + (175303/30)*n + (556181/10);
for n mod 60 = 10: a(n) = (3107/24)*n^2 + (109097/20)*n + (141317/3);
for n mod 60 = 11: a(n) = (10769/72)*n^2 + (977923/180)*n + (19746049/360).
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