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 A100230 Main diagonal of triangle A100229. 5
 1, 2, 10, 35, 118, 392, 1297, 4286, 14158, 46763, 154450, 510116, 1684801, 5564522, 18378370, 60699635, 200477278, 662131472, 2186871697, 7222746566, 23855111398, 78788080763, 260219353690, 859446141836, 2838557779201 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Let F(x) = Product_{n >= 1} (1 + x^(4*n + 1))/(1 - x^(4*n + 3)). Let alpha = (1/2)*(3 - sqrt(13)). This sequence occurs as partial numerators in the simple continued fraction expansion of the real number F(alpha) = 1.34372 29374 22358 27049 ... = 1 + 1/(2 + 1/(1 + 1/(10 + 1/(35 + 1/(1 + 1/(118 + 1/(392 + 1/(1 + ...)))))))). - Peter Bala, Oct 17 2019 LINKS Index entries for linear recurrences with constant coefficients, signature (4,-2,-1). FORMULA a(n) = 3*a(n-1) + a(n-2) + 3 for n>1, with a(0)=1, a(1)=2. G.f.: Sum_{n>=1} a(n)*x^n/n = log((1-x)/(1-3*x-x^2)). a(0)=1, a(1)=2, a(2)=10, a(n)=4*a(n-1)-2*a(n-2)-a(n-3). [Harvey P. Dale, May 06 2012] MATHEMATICA LinearRecurrence[{4, -2, -1}, {1, 2, 10}, 30] (* Harvey P. Dale, May 06 2012 *) PROG (PARI) a(n)=if(n==0, 1, n*polcoeff(log((1-x)/(1-3*x-x^2)+x*O(x^n)), n)) CROSSREFS Cf. A100228, A100229. Equals A006497(n) - 1. Sequence in context: A236377 A197556 A295133 * A220255 A146983 A327075 Adjacent sequences:  A100227 A100228 A100229 * A100231 A100232 A100233 KEYWORD nonn AUTHOR Paul D. Hanna, Nov 29 2004 STATUS approved

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Last modified April 18 03:59 EDT 2021. Contains 343072 sequences. (Running on oeis4.)