A132738 Row sums of triangle A132737.
1, 2, 7, 16, 33, 66, 131, 260, 517, 1030, 2055, 4104, 8201, 16394, 32779, 65548, 131085, 262158, 524303, 1048592, 2097169, 4194322, 8388627, 16777236, 33554453, 67108886, 134217751, 268435480, 536870937, 1073741850, 2147483675, 4294967324, 8589934621
Offset: 0
Examples
a(3) = 16 = sum of row 3 terms of triangle A132737: (1 + 7 + 7 + 1). a(3) = 16 = (1, 3, 3, 1) dot (1, 1, 4, 0) = (1 + 3 + 12 + 0).
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-5,2).
Crossrefs
Cf. A132737.
Programs
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Magma
[1] cat [2^(n+1) +n-3: n in [1..40]]; // G. C. Greubel, Feb 15 2021
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Mathematica
Join[{1,2,7}, Table[BitSet[n, (n+4)], {n,0,40}]] (* Vladimir Joseph Stephan Orlovsky, Jul 19 2011 *) Table[2^(n+1) +n-3 +2*Boole[n==0], {n,0,40}] (* G. C. Greubel, Feb 15 2021 *) -
PARI
Vec((1-2*x+4*x^2-4*x^3)/((1-x)^2*(1-2*x)) + O(x^40)) \\ Colin Barker, Mar 14 2014
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Sage
[1]+[2^(n+1) +n-3 for n in (1..40)] # G. C. Greubel, Feb 15 2021
Formula
Binomial transform of [1, 1, 4, 0, 4, 0, 4, ...].
a(n) = 2^(n+1) + n - 3 for n > 0. - Franklin T. Adams-Watters, Jul 06 2009
From Colin Barker, Mar 14 2014: (Start)
a(n) = 4*a(n-1) - 5*a(n-2) + 2*a(n-3) for n>3.
G.f.: (1 -2*x +4*x^2 -4*x^3)/((1-x)^2*(1-2*x)). (End)
E.g.f.: 2 - (3-x)*exp(x) + 2*exp(2*x). - G. C. Greubel, Feb 15 2021
Extensions
Extended by Franklin T. Adams-Watters, Jul 06 2009