A002570 From a definite integral.

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

Author

N. J. A. Sloane

Keywords

• nonn

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.

Programs

Maple

A002570:=-1/(z-1)/(z**2-3*z+1)/(1+z)**3; # conjectured by Simon Plouffe in his 1992 dissertation

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

Extensions

More terms from Sean A. Irvine, Apr 09 2014