OFFSET
0,1
REFERENCES
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
Richard K. Guy, Letter to N. J. A. Sloane, May 1990.
Richard K. Guy, Catwalks, sandsteps and Pascal pyramids, J. Integer Sequences, Vol. 3 (2000), Article 00.1.6 (see Figure 7).
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.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
G.f.: 4*(19-4*x+x^2)/(x-1)^4. - Simon Plouffe in his 1992 dissertation
a(n) = 4(n+1)(n+3)(8n+19)/3.
Sum_{n>=0} 1/a(n) = 499/1936 + (6*log(1+sqrt(2))*sqrt(2) - 3*(sqrt(2)-1)*Pi - 24*log(2))/55. - Amiram Eldar, Sep 10 2022
MATHEMATICA
a[n_] := 4 (n + 1) (n + 3) (8 n + 19)/3; Array[a, 30, 0] (* Amiram Eldar, Sep 10 2022 *)
PROG
(PARI) vector(40, n, n--; 4*(n+1)*(n+3)*(8*n+19)/3) \\ Michel Marcus, Oct 13 2014
CROSSREFS
KEYWORD
nonn,walk,easy
AUTHOR
STATUS
approved