OFFSET
1,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (2).
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
EXAMPLE
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.
MATHEMATICA
Rest@CoefficientList[Series[x*(1+x+x^2)/(1-2*x), {x, 0, 40}], x] (* Vincenzo Librandi, Oct 12 2013 *)
PROG
(PARI) concat([1, 3], vector(30, n, 7*2^(n-1))) \\ G. C. Greubel, Jun 05 2019
(Magma) [1, 3] cat [7*2^(n-3): n in [3..40]]; // G. C. Greubel, Jun 05 2019
(Sage) [1, 3]+[7*2^(n-3) for n in (3..40)] # G. C. Greubel, Jun 05 2019
(GAP) Concatenation([1, 3], List([3..40], n-> 7*2^(n-3))); # G. C. Greubel, Jun 05 2019
(Python) print([7*2**n//8 for n in range(1, 50)]) # Karl V. Keller, Jr., May 11 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Nov 22 2006
EXTENSIONS
More terms from N. J. A. Sloane, Dec 15 2007
STATUS
approved