login
A126284
a(n) = 5*2^n - 4*n - 5.
2
1, 7, 23, 59, 135, 291, 607, 1243, 2519, 5075, 10191, 20427, 40903, 81859, 163775, 327611, 655287, 1310643, 2621359, 5242795, 10485671, 20971427, 41942943, 83885979, 167772055, 335544211, 671088527, 1342177163, 2684354439
OFFSET
1,2
COMMENTS
Row sums of A125233.
A triangle with left and right borders being the odd numbers 1,3,5,7,... will give the same partial sums for the sum of its rows. - J. M. Bergot, Sep 29 2012
The triangle in the above comment is constructed the same way as Pascal's triangle, i.e., C(n, k) = C(n-1, k) + C(n-1, k-1). - Michael B. Porter, Oct 03 2012
FORMULA
a(1) = 1; a(2) = 7; a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3), n > 2.
The 6th diagonal from the right of A126277.
G.f.: x*(1+3*x)/(1-4*x+5*x^2-2*x^3). - Colin Barker, Feb 12 2012
E.g.f.: 5*exp(2*x) - (5+4*x)*exp(x). - G. C. Greubel, Oct 23 2018
MAPLE
A126284:=n->5*2^n-4*n-5; seq(A126284(n), n=1..50); # Wesley Ivan Hurt, Mar 27 2014
MATHEMATICA
CoefficientList[Series[(1 + 3 x)/(1 - 4 x + 5 x^2 - 2 x^3), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 28 2014 *)
PROG
(PARI) a(n)=5<<n-4*n-5 \\ Charles R Greathouse IV, Oct 03 2012
(Magma) [5*2^n - 4*n - 5: n in [1..30]]; // G. C. Greubel, Oct 23 2018
(GAP) List([1..30], n->5*2^n-4*n-5); # Muniru A Asiru, Oct 24 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Dec 24 2006
EXTENSIONS
More terms from Vladimir Joseph Stephan Orlovsky, Oct 18 2008
New definition from R. J. Mathar, Sep 29 2012
STATUS
approved