A081034 -id:A081034 - cp's OEIS frontend

A016178 Expansion of g.f. 1/((1 - 7x)*(1 - 9x)).

1, 16, 193, 2080, 21121, 206896, 1979713, 18640960, 173533441, 1602154576, 14701866433, 134294124640, 1222488408961, 11099284691056, 100571785292353, 909893629141120, 8222275592839681, 74233110849544336, 669726411243809473, 6038936596379658400, 54430221633714537601

Offset: 0

N. J. A. Sloane

Index entries for linear recurrences with constant coefficients, signature (16,-63).

Cf. A081034, A081202.

Join[{a=1,b=16},Table[c=16*b-63*a;a=b;b=c,{n,40}]] (* Vladimir Joseph Stephan Orlovsky, Feb 08 2011 *)
CoefficientList[Series[1/((1-7x)(1-9x)),{x,0,30}],x] (* or *) LinearRecurrence[ {16,-63},{1,16},30] (* Harvey P. Dale, Mar 11 2013 *)

a(n)=(9^n++-7^n)/2 \\ Charles R Greathouse IV, Sep 24 2012

a(n) = (9^(n+1) - 7^(n+1))/2 = A081202(n+1). Binomial transform of A081034. - R. J. Mathar, Sep 18 2008
From Vincenzo Librandi, Feb 09 2011: (Start)
a(n) = 9*a(n-1) + 7^n, with a(0)=1.
a(n) = 16*a(n-1) - 63*a(n-2), n >= 2. (End)
E.g.f.: exp(7*x)*(9*exp(2*x) - 7)/2. - Stefano Spezia, Jul 23 2024

a(18)-a(20) from Stefano Spezia, Jul 23 2024

A081035 8th binomial transform of the periodic sequence (1,9,1,1,9,1...).

Original entry on oeis.org

1, 17, 209, 2273, 23201, 228017, 2186609, 20620673, 192174401, 1775688017, 16304021009, 148995991073, 1356782533601, 12321773100017, 111671069983409, 1010465414433473, 9132169221980801, 82455386442384017, 743959522093353809, 6708663007623467873, 60469158230094196001

Offset: 0

Paul Barry, Mar 03 2003

Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (16,-63).

Cf. A081034, A081036.

[5*9^n-4*7^n: n in [0..25]]; // Vincenzo Librandi, Aug 06 2013

CoefficientList[Series[(1 + x)/((1 - 7 x) (1 - 9 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)
LinearRecurrence[{16,-63},{1,17},30] (* Harvey P. Dale, Oct 07 2014 *)

a(n)=5*9^n-4*7^n \\ Charles R Greathouse IV, Oct 07 2015

a(n) = 9*a(n-1) + 8*7^(n-1).
a(n) = 5*9^n - 4*7^n.
G.f.: (1+x)/((1-7*x)*(1-9*x)). - Vincenzo Librandi, Aug 06 2013
a(0)=1, a(1)=17, a(n)=16*a(n-1)-63*a(n-2). - Harvey P. Dale, Oct 07 2014
E.g.f.: exp(7*x)*(5*exp(2*x) - 4). - Stefano Spezia, Jul 23 2024

A081036 9th binomial transform of the periodic sequence (1,10,1,1,10,1...).

Original entry on oeis.org

1, 19, 262, 3196, 36568, 402544, 4320352, 45562816, 474502528, 4896020224, 50168161792, 511345294336, 5190762354688, 52526098837504, 530208790700032, 5341670325600256, 53733362604802048, 539866900838416384, 5418935206707331072, 54351481653658648576, 544811853229269188608

Offset: 0

Paul Barry, Mar 03 2003

Vincenzo Librandi, Table of n, a(n) for n = 0..300
Index entries for linear recurrences with constant coefficients, signature (18,-80).

Cf. A081034, A081035.

[(11/2)*10^n-(9/2)*8^n: n in [0..25]]; // Vincenzo Librandi, Aug 06 2013

CoefficientList[Series[(1 + x)/((1 - 8 x) (1 - 10 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Aug 06 2013 *)
LinearRecurrence[{18,-80},{1,19},20] (* Harvey P. Dale, Aug 16 2014 *)

a(n) = 10*a(n-1) + 9*8^(n-1).
a(n) = (11/2)*10^n - (9/2)*8^n.
G.f.: (1+x)/((1-8*x)*(1-10*x)). - Vincenzo Librandi, Aug 06 2013
a(0)=1, a(1)=19, a(n)=18*a(n-1)-80*a(n-2). - Harvey P. Dale, Aug 16 2014
E.g.f.: exp(8*x)*(11*exp(2*x) - 9)/2. - Stefano Spezia, Jul 23 2024

Corrected by T. D. Noe, Nov 07 2006

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A016178 Expansion of g.f. 1/((1 - 7x)*(1 - 9x)).

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A081035 8th binomial transform of the periodic sequence (1,9,1,1,9,1...).

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A081036 9th binomial transform of the periodic sequence (1,10,1,1,10,1...).

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Author

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Magma

Mathematica

Formula

Extensions