A125176 Row sums of A125175.
1, 3, 7, 14, 28, 56, 112, 224, 448, 896, 1792, 3584, 7168, 14336, 28672, 57344, 114688, 229376, 458752, 917504, 1835008, 3670016, 7340032, 14680064, 29360128, 58720256, 117440512, 234881024, 469762048, 939524096, 1879048192, 3758096384, 7516192768, 15032385536
Offset: 1
Examples
First few rows of A125175 are: 1; 1, 2; 1, 3, 3; 1, 4, 5, 4; .... a(4) = 1 + 4 + 5 + 4 = 14. a(6) = 1 + 6 + 14 + 20 + 9 + 6 = 56 = 7*8 = 7*2^3.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (2).
Programs
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GAP
Concatenation([1,3], List([3..40], n-> 7*2^(n-3))); # G. C. Greubel, Jun 05 2019
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Magma
[1,3] cat [7*2^(n-3): n in [3..40]]; // G. C. Greubel, Jun 05 2019
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Mathematica
Rest@CoefficientList[Series[x*(1+x+x^2)/(1-2*x), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 12 2013 *) -
PARI
concat([1,3], vector(30, n, 7*2^(n-1))) \\ G. C. Greubel, Jun 05 2019
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Python
print([7*2**n//8 for n in range(1, 50)]) # Karl V. Keller, Jr., May 11 2022
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Sage
[1,3]+[7*2^(n-3) for n in (3..40)] # G. C. Greubel, Jun 05 2019
Formula
a(1) = 1, a(2) = 3, a(n) = 7*2^(n-3) for n>=3.
From Colin Barker, Oct 12 2013: (Start)
a(n) = 2*a(n-1) for n>3.
G.f.: x*(1 + x + x^2)/(1-2*x). (End)
E.g.f.: (7*exp(2*x) - 7 - 6*x - 2*x^2)/8. - G. C. Greubel, Jun 05 2019
Extensions
More terms from N. J. A. Sloane, Dec 15 2007