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URL: https://oeis.org/A133086

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A133086
Row sums of triangle A133085.
2
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, 52076478464
OFFSET
0,2
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
From Elmo R. Oliveira, Mar 18 2026: (Start)
G.f.: (1 - 2*x^2 + 2*x^3)/(1 - 2*x)^2.
E.g.f.: (x + (2 + 3*x)*exp(2*x))/2.
a(n) = 4*(a(n-1) - a(n-2)) for n >= 4.
a(n) = 2*A098156(n) for n > 0. (End)
EXAMPLE
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).
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 *)
PROG
(PARI) concat([1, 4], for(n=2, 50, print1(2^n + 3*n*2^(n-2), ", "))) \\ G. C. Greubel, Oct 21 2017
(Magma) [1, 4] cat [2^n+3*n*2^(n-2): n in [2..30]]; // Vincenzo Librandi, Oct 21 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Sep 08 2007
STATUS
approved