A124671 Row sums of A126277 = binomial transform of (1, 2, 2, 3, 4, 4, 4, ...)

1, 3, 7, 16, 37, 85, 191, 418, 893, 1871, 3863, 7892, 16005, 32297, 64959, 130374, 261309, 523299, 1047415, 2095800, 4192741, 8386813, 16775167, 33552106, 67106237, 134214775, 268432151, 536867228, 1073737733, 2147479121, 4294962303, 8589929102, 17179863165

Offset: 1

Author

Gary W. Adamson, Dec 23 2006

Keywords

• nonn
• easy

Examples

			a(4) = 16 = sums of 4th row terms of A126277: (1 + 4 + 7 + 4).
a(4) = 16 = 1*1 + 3*2 + 3*2 + 1*3.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (6,-14,16,-9,2).

Crossrefs

Cf. A126277.

Programs

Magma

I:=[1,3,7,16,37]; [n le 5 select I[n] else 6*Self(n-1)-14*Self(n-2)+16*Self(n-3)-9*Self(n-4)+2*Self(n-5): n in [1..40]]; // Vincenzo Librandi, Mar 15 2014

Mathematica

CoefficientList[Series[(1 - 3 x + 3 x^2)/((1 - 2 x) (x - 1)^4), {x, 0, 40}], x] (* Vincenzo Librandi, Mar 15 2014 *)

PARI

Vec(x*(1-3*x+3*x^2)/((1-2*x)*(x-1)^4) + O(x^100)) \\ Colin Barker, Mar 13 2014

Formula

G.f.: x*(1-3*x+3*x^2)/((1-2*x)*(x-1)^4). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 14 2009; corrected by R. J. Mathar, Sep 16 2009

a(n) = 6*a(n-1) - 14*a(n-2) + 16*a(n-3) - 9*a(n-4) + 2*a(n-5) for n > 4. - Vincenzo Librandi, Mar 15 2014

a(n) = -2 + 2^(1+n) - (5*n)/6 - n^3/6. - Colin Barker, Jul 21 2017

Extensions

More terms from Colin Barker, Mar 13 2014