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A132734 Row sums of triangle A132733. 2
1, 2, 5, 16, 43, 102, 225, 476, 983, 2002, 4045, 8136, 16323, 32702, 65465, 130996, 262063, 524202, 1048485, 2097056, 4194203, 8388502, 16777105, 33554316, 67108743, 134217602, 268435325, 536870776, 1073741683, 2147483502, 4294967145, 8589934436, 17179869023 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Andrew Howroyd, 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, 2, 6, 2, 6, 2, 6, ...].

From Andrew Howroyd, Sep 01 2018: (Start)

a(n) = 4*2^n - 5*n - 1 for n > 0.

a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) for n > 3.

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

E.g.f.: -2 - (1 + 5*x)*exp(x) + 4*exp(2*x). - G. C. Greubel, Feb 14 2021

EXAMPLE

a(3) = 16 = sum of row 3 terms of triangle A132733: (1 + 7 + 7 + 1).

a(3) = 16 = (1, 3, 3, 1) dot (1, 1, 2, 6) = (1 + 3 + 6 + 6).

MATHEMATICA

Table[2^(n+2) -(5*n+1) -2*Boole[n==0], {n, 0, 30}] (* G. C. Greubel, Feb 14 2021 *)

PROG

(PARI) a(n)={if(n==0, 1, 4*2^n - 5*n - 1)} \\ Andrew Howroyd, Sep 01 2018

(PARI) Vec((1 - 2*x + 2*x^2 + 4*x^3)/((1 - x)^2*(1 - 2*x)) + O(x^40)) \\ Andrew Howroyd, Sep 01 2018

(Sage) [1]+[2^(n+2) -(5*n +1) for n in (1..30)] # G. C. Greubel, Feb 14 2021

(Magma) [1] cat [2^(n+2) -(5*n +1): n in [1..30]]; // G. C. Greubel, Feb 14 2021

CROSSREFS

Cf. A132733.

Sequence in context: A148371 A148372 A148373 * A148374 A182884 A152428

Adjacent sequences:  A132731 A132732 A132733 * A132735 A132736 A132737

KEYWORD

nonn,easy

AUTHOR

Gary W. Adamson, Aug 26 2007

EXTENSIONS

Terms a(10) and beyond from Andrew Howroyd, Sep 01 2018

STATUS

approved

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Last modified October 6 09:29 EDT 2022. Contains 357263 sequences. (Running on oeis4.)