|
Search: id:A101854
|
|
|
| A101854 |
|
5th partial summation within series as series accumulate n times from an initial sequence of Euler Triangle's row 3: 1,4,1. |
|
+0
1
|
|
| 6, 24, 61, 125, 225, 371, 574, 846, 1200, 1650, 2211, 2899, 3731, 4725, 5900, 7276, 8874, 10716, 12825, 15225, 17941, 20999, 24426, 28250, 32500, 37206, 42399, 48111, 54375, 61225, 68696, 76824, 85646, 95200, 105525, 116661, 128649, 141531, 155350
(list; graph; listen)
|
|
|
OFFSET
|
1,1
|
|
|
LINKS
|
C. Rossiter, Depictions, Explorations and Formulas of the Euler/Pascal Cube.
|
|
FORMULA
|
a(1)=1; a(n) = (25*n)/12 + (71*n^2)/24 + (11*n^3)/12 + n^4/24
G.f.: x*(6-6*x+x^2)/(1-x)^5 [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
|
|
EXAMPLE
|
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 <- 5th
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
|
|
CROSSREFS
|
Sequence in context: A160936 A007531 A130669 this_sequence A101877 A092348 A006528
Adjacent sequences: A101851 A101852 A101853 this_sequence A101855 A101856 A101857
|
|
KEYWORD
|
easy,nonn,uned
|
|
AUTHOR
|
Cecilia Rossiter (cecilia(AT)noticingnumbers.net), Dec 18 2004
|
|
EXTENSIONS
|
G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.
|
|
|
Search completed in 0.002 seconds
|
