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A124671 Row sums of A126277 = binomial transform of (1, 2, 2, 3, 4, 4, 4,...) 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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).

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

EXAMPLE

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.

MATHEMATICA

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

PROG

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

(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

CROSSREFS

Cf. A126277.

Sequence in context: A033303 A078056 A173761 * A188626 A123392 A095263

Adjacent sequences:  A124668 A124669 A124670 * A124672 A124673 A124674

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Dec 23 2006

EXTENSIONS

More terms from Colin Barker, Mar 13 2014

STATUS

approved

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Last modified August 17 22:59 EDT 2019. Contains 326059 sequences. (Running on oeis4.)