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A137280 a(n) = 3*a(n-1) + 7*a(n-2). 0
1, 10, 37, 181, 802, 3673, 16633, 75610, 343261, 1559053, 7079986, 32153329, 146019889, 663132970, 3011538133, 13676545189, 62110402498, 282067023817, 1280973888937, 5817390833530, 26418989723149, 119978705004157 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) == 1 mod 9.

a(n)/a(n-1) tends to 4.54138126... = (3 + sqrt(37))/2

LINKS

Table of n, a(n) for n=1..22.

Index entries for linear recurrences with constant coefficients, signature (3,7)

FORMULA

a(1) = 1, a(2) = 10, a(n), n>2 = 3*a(n-1) + 7*a(n-2). a(n) = upper left term in [1,3; 3,2]^n

O.g.f.: x*(1+7*x)/(1-3*x-7*x^2) . a(n)=A015524(n)+7*A015524(n-1). - R. J. Mathar, Mar 17 2008

a(n)=-17/74*(3/2-1/2*sqrt(37))^n*sqrt(37)+1/2*(3/2-1/2*sqrt(37))^n+17/74*sqrt(37)*(3 /2+1/2*sqrt(37))^n+1/2*(3/2+1/2*sqrt(37))^n, with n>=0 - Paolo P. Lava, Jun 03 2008

EXAMPLE

a(4) = 181 = 3*a(3) + 7*a(2) = 3*37 + 7*10.

a(4) = 181 = upper left term in [1,3; 3,2]^4.

CROSSREFS

Sequence in context: A199208 A110528 A208674 * A071261 A129426 A215881

Adjacent sequences:  A137277 A137278 A137279 * A137281 A137282 A137283

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Mar 14 2008

STATUS

approved

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Last modified November 24 07:14 EST 2020. Contains 338607 sequences. (Running on oeis4.)