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Search: id:A101853
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| A101853 |
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4th partial summation within series as series accumulate n times from an initial sequence of Euler Triangle's row 3: 1,4,1. |
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+0
1
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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; listen)
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OFFSET
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1,1
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LINKS
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C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.
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FORMULA
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a(1)=1; a(n) = (10*z)/3 + (5*z^2)/2 + z^3/6
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EXAMPLE
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n = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ...
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
0 6 18 37 64 100 146 203 272 354 450 <- 4th
0 6 24 61 125 225 371 574 846 1200 1650
0 6 30 91 216 441 812 1386 2232 3432 5082
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
... ... ... ... ... ... ... ... ... ...
of each of the series
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CROSSREFS
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Sequence in context: A028896 A034857 A116367 this_sequence A132432 A005899 A129863
Adjacent sequences: A101850 A101851 A101852 this_sequence A101854 A101855 A101856
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KEYWORD
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easy,nonn,uned
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AUTHOR
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Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 18 2004
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