A016161
Expansion of g.f. 1/((1-5*x)*(1-7*x)).
Original entry on oeis.org
1, 12, 109, 888, 6841, 51012, 372709, 2687088, 19200241, 136354812, 964249309, 6798573288, 47834153641, 336059778612, 2358521965909, 16540171339488, 115933787267041, 812299450322412, 5689910849522509
Offset: 0
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[n le 2 select 12^(n-1) else 12*Self(n-1) -35*Self(n-2): n in [1..30]]; // G. C. Greubel, Nov 09 2024
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CoefficientList[Series[1/((1-5x)(1-7x)),{x,0,30}],x] (* or *) LinearRecurrence[ {12,-35},{1,12},30] (* Harvey P. Dale, Nov 16 2021 *)
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Vec(1/((1-5*x)*(1-7*x))+O(x^99)) \\ Charles R Greathouse IV, Sep 24 2012
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A016161=BinaryRecurrenceSequence(12,-35,1,12)
[A016161(n) for n in range(31)] # G. C. Greubel, Nov 09 2024
A191466
a(n) = 9^n - 5^n.
Original entry on oeis.org
0, 4, 56, 604, 5936, 55924, 515816, 4704844, 42656096, 385467364, 3477018776, 31332231484, 282185395856, 2540645125204, 22870688939336, 205860614516524, 1852867600961216, 16676418760213444, 150090820599733496, 1350832644186663964, 12157570091625288176, 109418512294354156084
Offset: 0
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[9^n-5^n: n in [0..20]];
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Table[9^n - 5^n, {n, 0, 25}] (* or *) CoefficientList[Series[4 x/((1 - 5 x) (1 - 9 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 05 2014 *)
LinearRecurrence[{14,-45},{0,4},20] (* Harvey P. Dale, Jun 26 2019 *)
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a(n)=9^n-5^n \\ Charles R Greathouse IV, Jun 08 2011
A017897
Expansion of 1/((1-3*x)*(1-5*x)*(1-9*x)).
Original entry on oeis.org
1, 17, 202, 2090, 20251, 189707, 1745332, 15900020, 144066901, 1301455397, 11737424062, 105758621150, 952437144751, 8574983669087, 77190104636392, 694787214149480, 6253466332501801, 56283104147438777, 506557473488982322, 4559064943373269010
Offset: 0
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Christian Brouder, William J. Keith, and Ângela Mestre, Closed forms for a multigraph enumeration, arXiv preprint arXiv:1301.0874 [math.CO], 2013-2015.
- Index entries for linear recurrences with constant coefficients, signature (17,-87,135).
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m:=20; R:=PowerSeriesRing(Integers(), m); Coefficients(R!(1/((1-3*x)*(1-5*x)*(1-9*x)))); // Vincenzo Librandi, Jul 01 2013
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I:=[1, 17, 202]; [n le 3 select I[n] else 17*Self(n-1)-87*Self(n-2)+135*Self(n-3): n in [1..20]]; // Vincenzo Librandi, Jul 01 2013
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a:= n -> (Matrix(3, (i,j)-> if (i=j-1) then 1 elif j=1 then [17, -87, 135][i] else 0 fi)^n)[1,1]: seq (a(n), n=0..25); # Alois P. Heinz, Aug 04 2008
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CoefficientList[Series[1 / ((1 - 3 x) (1 - 5 x) (1 - 9 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 01 2013 *)
LinearRecurrence[{17,-87,135},{1,17,202},30] (* Harvey P. Dale, Sep 26 2014 *)
a[n_]:=(9^(n+2) - 3*5^(n+2) + 2*3^(n+2))/24; Array[a, 30, 0] (* Stefano Spezia, Oct 04 2018 *)
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a(n) = (9^(n+2) - 3*5^(n+2) + 2*3^(n+2))/24; \\ Joerg Arndt, Aug 13 2013
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def A017897(n): return (9^(n+2) -3*5^(n+2) +2*3^(n+2))//24
[A017897(n) for n in range(41)] # G. C. Greubel, Nov 09 2024
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