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A132730 Row sums of triangle A132729. 2
1, 2, 3, 8, 21, 50, 111, 236, 489, 998, 2019, 4064, 8157, 16346, 32727, 65492, 131025, 262094, 524235, 1048520, 2097093, 4194242, 8388543, 16777148, 33554361, 67108790, 134217651, 268435376, 536870829 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (4,-5,2).

FORMULA

Binomial transform of [1, 1, 0, 4, 0, 4, 0, 4, ...].

a(n) = 2^(n+1) - 3*n + 1, for n > 0. - R. J. Mathar, Apr 04 2012

From G. C. Greubel, Feb 14 2021: (Start)

G.f.: (1 - 2*x + 4*x^3)/((1-x)^2 * (1-2*x)).

E.g.f.: -2 + (1-3*x)*exp(x) + 2*exp(2*x). (End)

EXAMPLE

a(4) = 21 = sum of row 4 terms of triangle A132729: (1 + 5 + 9 + 5 + 1).

a(3) = 8 = (1, 3, 3, 1) dot (1, 1, 0, 4) = (1 + 3 + 0 + 4).

MATHEMATICA

LinearRecurrence[{4, -5, 2}, {1, 2, 3, 8}, 30] (* Harvey P. Dale, Dec 30 2015 *)

Table[2^(n+1) -3*n +1 -2*Boole[n==0], {n, 0, 30}] (* G. C. Greubel, Feb 14 2021 *)

PROG

(Sage) [1]+[2^(n+1) -3*n +1 for n in (1..30)] # G. C. Greubel, Feb 14 2021

(Magma) [1] cat [2^(n+1) -3*n +1: n in [0..30]]; // G. C. Greubel, Feb 14 2021

CROSSREFS

Cf. A132729.

Sequence in context: A251608 A288252 A122263 * A004790 A245464 A243562

Adjacent sequences:  A132727 A132728 A132729 * A132731 A132732 A132733

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Aug 26 2007

STATUS

approved

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Last modified July 29 23:58 EDT 2021. Contains 346346 sequences. (Running on oeis4.)