A133086 Row sums of triangle A133085.
1, 4, 10, 26, 64, 152, 352, 800, 1792, 3968, 8704, 18944, 40960, 88064, 188416, 401408, 851968, 1802240, 3801088, 7995392, 16777216, 35127296, 73400320, 153092096, 318767104, 662700032, 1375731712, 2852126720, 5905580032, 12213813248, 25232932864
Offset: 0
Keywords
Examples
a(3) = 26 = sum of row 3 of triangle A133085: (12 + 8, + 5 + 1). a(3) = 26 = (1, 3, 3, 1) dot (1, 3, 3, 7) = (1 + 9 + 9 + 7).
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-4).
Programs
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Magma
[1,4] cat [2^n+3*n*2^(n-2): n in [2..30]]; // Vincenzo Librandi, Oct 21 2017
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Mathematica
Join[{1, 4}, Table[2^n + 3*n*2^(n - 2), {n, 2, 50}]] (* G. C. Greubel, Oct 21 2017 *) LinearRecurrence[{4,-4},{1,4,10,26},40] (* Harvey P. Dale, Jul 19 2020 *) -
PARI
concat([1,4], for(n=2,50, print1(2^n + 3*n*2^(n-2), ", "))) \\ G. C. Greubel, Oct 21 2017
Formula
Binomial transform of A114753: (1, 3, 3, 7, 5, 11, 7, 15, ...).
For n>1, a(n) = 2^n + 3*n*2^(n-2). - R. J. Mathar, Apr 04 2012