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A002309
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Sum of fourth powers of odd numbers.
(Formerly M5359 N2327)
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| 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.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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
| a(n)=(48*n^5-40*n^3+7*n)/15. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Jan 29 2003
a(1)=1, a(2)=82, a(3)=707, a(4)=3108, a(5)=9669, a(6)=24310, a(n)= 6*a(n-1)- 15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6) [From Harvey P. Dale, Oct 24 2011]
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MAPLE
| 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
| 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]
Accumulate[Range[1, 63, 2]^4] (* From Harvey P. Dale, Oct 24 2011 *)
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CROSSREFS
| Cf. A002593.
Sequence in context: A082972 A031422 A186688 * A128959 A173356 A083386
Adjacent sequences: A002306 A002307 A002308 * A002310 A002311 A002312
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KEYWORD
| nonn,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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