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A152262 a(n) = 14*a(n-1) - 43*a(n-2), n > 1; a(0)=1, a(1)=7. 3
1, 7, 55, 469, 4201, 38647, 360415, 3383989, 31878001, 300780487, 2840172775, 26828857909, 253476581401, 2395031249527, 22630944493135, 213846879174229, 2020725695234401, 19094743928789767, 180435210107977495 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A145301. Inverse binomial transform of A152263. - Philippe Deléham, Dec 03 2008

REFERENCES

H. D. Nguyen, D. Taggart, Mining the OEIS: Ten Experimental Conjectures, 2013; http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.391.2522&rep=rep1&type=pdf. Mentions this sequence. - From N. J. A. Sloane, Mar 16 2014

LINKS

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (14,-43).

FORMULA

a(n) = ((7 + sqrt(6))^n + (7 - sqrt(6))^n)/2.

From Philippe Deléham, Dec 03 2008: (Start)

G.f.: (1-7*x)/(1-14*x+43*x^2).

a(n) = Sum_{k=0..n} A098158(n,k)*7^(2k-n)*6^(n-k). (End)

a(n) = Sum_{k=0..n} A027907(n,2k)*6^k. - J. Conrad, Aug 24 2016

E.g.f.: cosh(sqrt(6)*x)*exp(7*x). - Ilya Gutkovskiy, Aug 24 2016

MATHEMATICA

LinearRecurrence[{14, -43}, {1, 7}, 30] (* Harvey P. Dale, Apr 26 2015 *)

PROG

(MAGMA) Z<x>:= PolynomialRing(Integers()); N<r6>:=NumberField(x^2-6); S:=[ ((7+r6)^n+(7-r6)^n)/2: n in [0..18] ]; [ Integers()!S[j]: j in [1..#S] ]; // Klaus Brockhaus, Dec 03 2008

CROSSREFS

Sequence in context: A096951 A113714 A246459 * A078018 A108628 A116862

Adjacent sequences:  A152259 A152260 A152261 * A152263 A152264 A152265

KEYWORD

nonn,easy

AUTHOR

Al Hakanson (hawkuu(AT)gmail.com), Dec 01 2008

EXTENSIONS

Name from Philippe Deléham, Dec 03 2008

STATUS

approved

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Last modified April 19 06:30 EDT 2019. Contains 322237 sequences. (Running on oeis4.)