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A002570
From a definite integral.
(Formerly M4090 N1698)
2
1, 1, 6, 11, 36, 85, 235, 600, 1590, 4140, 10866, 28416, 74431, 194821, 510096, 1335395, 3496170, 9153025, 23963005, 62735880, 164244756, 429998256, 1125750156, 2947252056, 7716006181, 20200766305, 52886292930, 138458112275, 362488044120
OFFSET
1,3
REFERENCES
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).
LINKS
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
L. R. Shenton, A determinantal expansion for a class of definite integral. Part 5. Recurrence relations, Proc. Edinburgh Math. Soc. (2) 10 (1957), 167-188.
L. R. Shenton and K. O. Bowman, Second order continued fractions and Fibonacci numbers, Far East Journal of Applied Mathematics, 20(1), 17-31, 2005.
FORMULA
a(n) = a(n-2) + A002571(n-1), n > 2. - Sean A. Irvine, Apr 09 2014
a(2*n-2) = Sum_{k=0..n} k*Fibonacci(2*n-2*k), n > 1. - Greg Dresden, Dec 02 2021
MAPLE
A002570:=-1/(z-1)/(z**2-3*z+1)/(1+z)**3; # conjectured by Simon Plouffe in his 1992 dissertation
CROSSREFS
Sequence in context: A130667 A259669 A108698 * A038265 A243139 A288822
KEYWORD
nonn
EXTENSIONS
More terms from Sean A. Irvine, Apr 09 2014
STATUS
approved