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A140063 Binomial transform of [1, 3, 7, 0, 0, 0,...]. 1
1, 4, 14, 31, 55, 86, 124, 169, 221, 280, 346, 419, 499, 586, 680, 781, 889, 1004, 1126, 1255, 1391, 1534, 1684, 1841, 2005, 2176, 2354, 2539, 2731, 2930, 3136, 3349, 3569, 3796, 4030, 4271, 4519, 4774, 5036 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..39.

Derek Kinsella, Plane division by lines and circles

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

A007318 * [1, 3, 7, 0, 0, 0,...].

O.g.f.: x*(1+x+5x^2)/(1-x)^3. - R. J. Mathar, May 06 2008

a(n) = 7*n^2/2-15*n/2+5 = 3*a(n-1)-3*a(n-2)+a(n-3). [From R. J. Mathar, Jul 31 2009]

a(n)=a(n-1)+7*n-11 (with a(1)=1) [From Vincenzo Librandi, Nov 24 2010]

EXAMPLE

a(4) = 31 = (1, 3, 3, 1) dot (1, 3, 7, 0) = (1 + 9 + 21 + 0).

MATHEMATICA

s = 1; lst = {s}; Do[s += n + 2; AppendTo[lst, s], {n, 1, 265, 7}]; lst [From Zerinvary Lajos, Jul 11 2009]

CROSSREFS

Sequence in context: A049451 A079776 A117109 * A051409 A072475 A001740

Adjacent sequences:  A140060 A140061 A140062 * A140064 A140065 A140066

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, May 03 2008

EXTENSIONS

More terms from R. J. Mathar, May 06 2008

STATUS

approved

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Last modified May 26 12:21 EDT 2017. Contains 287095 sequences.