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
Examples
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).
Links
- Andrew Howroyd, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-5,2)
Crossrefs
Cf. A132733.
Programs
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Magma
[1] cat [2^(n+2) -(5*n +1): n in [1..30]]; // G. C. Greubel, Feb 14 2021
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Mathematica
Table[2^(n+2) -(5*n+1) -2*Boole[n==0], {n,0,30}] (* G. C. Greubel, Feb 14 2021 *) -
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
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Sage
[1]+[2^(n+2) -(5*n +1) for n in (1..30)] # G. C. Greubel, Feb 14 2021
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
Extensions
Terms a(10) and beyond from Andrew Howroyd, Sep 01 2018