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Search: id:A137774
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| A137774 |
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Recurrences family for sequences identical to their fourth differences:a(n)=k*a(n-1)+(10-4k)*a(n-2)+(6k-20)*a(n-3)+(16-4k)*a(n-4),n grth 4,k=4 excluded.Last 0's not written in a(n).Here k nonnegative;Consider princeps sequence A000749: 0, 0, 0, 1, 4, 10, 20, 36, 64, 120 .. .From 0, 0, 0, 1, 4 every k gives A000749.Examples; k=2: a(n)=2a(n-1)+2a(n-2)-8a(n-3)+8a(n-4),k=3: a(n)=3a(n-1)-2a(n-2)-2a(n-3)+4a(n-4),k=4: 4a(n-1)-6a(n-2)+4a(n-3), A038503,A038504,A038505 and many others,k=5:a(n)=5a(n-1)-10a(n-2)+10a(n-3)-4a(n-4),k=6:a(n)=6a(n-1)-14a(n-2)+16a(n-3)-8a(n-4),A099855,A038504,A135035. |
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| 0, 10, -20, 16, 1, 6, -14, 12, 2, 2, -8, 8, 3, -2, -2, 4, 4, -6, 4, 0, 5, -10, 10, -4, 6, -14, 16, -8, 7, -18, 22, -12
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