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Search: id:A101855
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| A101855 |
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6th 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, 30, 91, 216, 441, 812, 1386, 2232, 3432, 5082, 7293, 10192, 13923, 18648, 24548, 31824, 40698, 51414, 64239, 79464, 97405, 118404, 142830, 171080, 203580, 240786, 283185, 331296, 385671, 446896, 515592, 592416, 678062, 773262, 878787, 995448
(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) = (23*n)/15 + (11*n^2)/4 + (35*n^3)/24 + n^4/4 + n^5/120
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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
0 6 24 61 125 225 371 574 846 1200 1650
0 6 30 91 216 441 812 1386 2232 3432 5082 <- 6th
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: A033487 A061138 A073948 this_sequence A101375 A074007 A152573
Adjacent sequences: A101852 A101853 A101854 this_sequence A101856 A101857 A101858
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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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