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A101853
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n*(20+15*n+n^2)/6.
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3
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6, 18, 37, 64, 100, 146, 203, 272, 354, 450, 561, 688, 832, 994, 1175, 1376, 1598, 1842, 2109, 2400, 2716, 3058, 3427, 3824, 4250, 4706, 5193, 5712, 6264, 6850, 7471, 8128, 8822, 9554, 10325, 11136, 11988, 12882, 13819, 14800
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 4th partial summation within series as series accumulate n times from an initial sequence of Euler Triangle's row 3: 1,4,1. The 1,4,1 is the left column, A101101 the second column, A008458 the third, A003215 the fourth column etc of the array in the example. a(n) is the 4th row.
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LINKS
| C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
| Gf. x*(6-6*x+x^2) / (x-1)^4 . - R. J. Mathar, Dec 06 2011
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EXAMPLE
| Left column the third row of A008292, and subsequent columns defined as partial sums along their preceding neighbours:
1 1 1 1 1 1 1 1 1 1 1
4 5 6 7 8 9 10 11 12 13 14
1 6 12 19 27 36 46 57 69 82 96 A051936
0 6 18 37 64 100 146 203 272 354 450 A101853
0 6 24 61 125 225 371 574 846 1200 1650 A101854
0 6 30 91 216 441 812 1386 2232 3432 5082 A101855
0 6 36 127 343 784 1596 2982 5214 8646 13728
0 6 42 169 512 1296 2892 5874 11088 19734 33462
0 6 48 217 729 2025 4917 10791 21879 41613 75075
... ... ... ... ... ... ... ... ... ...
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CROSSREFS
| Sequence in context: A180438 A202366 A185223 * A132432 A005899 A180118
Adjacent sequences: A101850 A101851 A101852 * A101854 A101855 A101856
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KEYWORD
| easy,nonn
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AUTHOR
| Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 18 2004
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