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A132074 Row sums of triangle A132073. 2
1, 4, 9, 16, 27, 46, 81, 148, 279, 538, 1053, 2080, 4131, 8230, 16425, 32812, 65583, 131122, 262197, 524344, 1048635, 2097214, 4194369, 8388676, 16777287, 33554506, 67108941, 134217808, 268435539, 536870998, 1073741913, 2147483740 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-5,2). [From R. J. Mathar, May 21 2010]

FORMULA

Binomial transform of [1, 3, 2, 0, 2, 0, 2, 0, 2,...].

G.f.:= (2*x^2+2*x^3-1)/((2*x-1)*(x-1)^2). a(n) = 2^n+3*n-1, n>0. [From R. J. Mathar, May 21 2010]

a(n) = 4*a(n-1) -5*a(n-2) +2*a(n-3). - Vincenzo Librandi, Jul 06 2012

EXAMPLE

a(4) = 27 = sum of row 4 terms of triangle A132073: (5 + 5 + 7 + 5 + 5).

a(4) = 27 = (1, 4, 6, 4, 1) dot (1, 3, 2, 0, 2) = (1 + 12 + 12 + 0 + 2).

MATHEMATICA

CoefficientList[Series[(2*x^2+2*x^3-1)/((2*x-1)*(x-1)^2), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 06 2012 *)

PROG

(MAGMA) I:=[1, 4, 9, 16]; [n le 4 select I[n] else 4*Self(n-1)-5*Self(n-2)+2*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Jul 06 2012

CROSSREFS

Cf. A132073.

Sequence in context: A029896 A301198 A009862 * A283549 A137354 A113495

Adjacent sequences:  A132071 A132072 A132073 * A132075 A132076 A132077

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Aug 09 2007

EXTENSIONS

More terms from R. J. Mathar, May 21 2010

STATUS

approved

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Last modified January 27 08:21 EST 2022. Contains 350606 sequences. (Running on oeis4.)