0,3

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).

A. Tarn, Approximations to certain square roots and the series of numbers connected therewith, Mathematical Questions and Solutions from the Educational Times, 1 (1916), 8-12.

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.

E.g.f. : exp(x)sinh(sqrt(10)x)/sqrt(10); a(n)=sum{k=0..n, binomial(n, 2k+1)10^k}. - Paul Barry (pbarry(AT)wit.ie), Sep 29 2004

a(n)=((1+sqrt(10))^n-(1-sqrt(10))^n)/(2Sqrt(10)) - Artur Jasinski (grafix(AT)csl.pl), Dec 10 2006

A002534:=-z/(-1+2*z+9*z**2); [S. Plouffe in his 1992 dissertation.]

Table[((1 + Sqrt[10])^n - (1 - Sqrt[10])^n)/(2Sqrt[10]), {n, 0, 30}]] - Artur Jasinski (grafix(AT)csl.pl), Dec 10 2006

(Other) sage: [lucas_number1(n, 2, -9) for n in xrange(0, 20)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]

Sequence in context: A102296 A025194 A084156 this_sequence A117717 A005584 A072416

Adjacent sequences: A002531 A002532 A002533 this_sequence A002535 A002536 A002537

nonn

N. J. A. Sloane (njas(AT)research.att.com).