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A154999 a(n) = 7*a(n-1) + 42*a(n-2), n>2; a(0)=1, a(1)=1, a(2)=13. 6
1, 1, 13, 133, 1477, 15925, 173509, 1883413, 20471269, 222402229, 2416608901, 26257155925, 285297665317, 3099884206069, 33681691385797, 365966976355477, 3976399872691813, 43205412115772725, 469446679463465221 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

The sequences A155001, A155000, A154999, A154997 and A154996 have a common form: a(0)=a(1)=1, a(2)= 2*b+1, a(n) = (b+1)*(a(n-1) + b*a(n-2)), with b some constant. The generating function of these is (1 - b*x - b^2*x^2)/(1 - (b+1)*x - b*(1+b)*x^2). - R. J. Mathar, Jan 20 2009

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..950

Index entries for linear recurrences with constant coefficients, signature (7,42).

FORMULA

a(n+1) = Sum_{k=0..n} A154929(n,k)*6^(n-k).

a(n) = (19/434)*sqrt(217)*(((7 + sqrt(217))/2)^(n-1) - ((7 - sqrt(217))/2)^(n-1)) +(1/2)*(((7 + sqrt(217))/2)^(n-1) + ((7 - sqrt(217))/2)^(n-1)) + (6/7)*(C(2*n,n) mod 2), with n >= 0. - Paolo P. Lava, Jan 20 2009

G.f.: (1 - 6*x - 36*x^2)/(1 - 7*x - 42*x^2). - G. C. Greubel, Apr 20 2021

MATHEMATICA

LinearRecurrence[{7, 42}, {1, 1, 13}, 31] (* G. C. Greubel, Apr 20 2021 *)

CoefficientList[Series[(1-6x-36x^2)/(1-7x-42x^2), {x, 0, 20}], x] (* Harvey P. Dale, Jan 14 2022 *)

PROG

(Magma) I:=[1, 13]; [1] cat [n le 2 select I[n] else 7*(Self(n-1) +6*Self(n-2)): n in [1..30]]; // G. C. Greubel, Apr 20 2021

(Sage)

def A154999_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P( (1-6*x-36*x^2)/(1-7*x-42*x^2) ).list()

A154999_list(30) # G. C. Greubel, Apr 20 2021

CROSSREFS

Cf. A154929, A154996, A154997, A155000, A155001.

Sequence in context: A031138 A097166 A073556 * A228277 A221153 A297335

Adjacent sequences:  A154996 A154997 A154998 * A155000 A155001 A155002

KEYWORD

nonn

AUTHOR

Philippe Deléham, Jan 18 2009

EXTENSIONS

More terms from Philippe Deléham, Jan 27 2009

Corrected by D. S. McNeil, Aug 20 2010

STATUS

approved

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Last modified October 6 12:35 EDT 2022. Contains 357264 sequences. (Running on oeis4.)