A132734 Row sums of triangle A132733.

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

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