A002570 From a definite integral. (Formerly M4090 N1698)

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

Table of n, a(n) for n=1..29.

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

Adjacent sequences: A002567 A002568 A002569 * A002571 A002572 A002573

Keyword

nonn

Author

N. J. A. Sloane

Extensions

More terms from Sean A. Irvine, Apr 09 2014

Status

approved