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Search: id:A002309
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| A002309 |
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Sum of fourth powers of odd numbers.
(Formerly M5359 N2327)
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+0
2
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| 1, 82, 707, 3108, 9669, 24310, 52871, 103496, 187017, 317338, 511819, 791660, 1182285, 1713726, 2421007, 3344528, 4530449, 6031074, 7905235, 10218676, 13044437, 16463238, 20563863, 25443544, 31208345, 37973546, 45864027, 55014652, 65570653, 77688014
(list; graph; listen)
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OFFSET
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1,2
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
J. L. Bailey, Jr., A table to facilitate the fitting of certain logistic curves, Annals Math. Stat., 2 (1931), 355-359.
F. E. Croxton and D. J. Cowden, Applied General Statistics. 2nd ed., Prentice-Hall, Englewood Cliffs, NJ, 1955, p. 742.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
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FORMULA
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a(n)=(48*n^5-40*n^3+7*n)/15. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 29 2003
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MAPLE
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A002309:=(1+76*z+230*z**2+76*z**3+z**4)/(z-1)**6; [Conjectured by S. Plouffe in his 1992 dissertation.]
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MATHEMATICA
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Table[(48*n^5 - 40*n^3 + 7*n)/15, {n, 0, 40}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 10 2006
s = 0; lst = {s}; Do[s += n^4; AppendTo[lst, s], {n, 1, 60, 2}]; lst [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 12 2009]
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CROSSREFS
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Cf. A002593.
Adjacent sequences: A002306 A002307 A002308 this_sequence A002310 A002311 A002312
Sequence in context: A005972 A082972 A031422 this_sequence A128959 A160914 A083386
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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