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A114119 Row sums of triangle A114118. 2
1, 3, 5, 6, 8, 9, 11, 12, 14, 15, 17, 18, 20, 21, 23, 24, 26, 27, 29, 30, 32, 33, 35, 36, 38, 39, 41, 42, 44, 45, 47, 48, 50, 51, 53, 54, 56, 57, 59, 60, 62, 63, 65, 66, 68, 69, 71, 72, 74, 75, 77, 78, 80, 81, 83, 84, 86, 87, 89, 90, 92, 93, 95, 96, 98, 99, 101, 102, 104, 105 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Taken modulo 3 yields 1,0,2,0,2,0,2,0,2,...; a(n) is congruent to 0 or 2 (mod 3) for n > 0.
LINKS
FORMULA
a(n) = 3*floor((n + 1)/2) + 2*((n+1) mod 2) - 0^n.
a(n) = Sum_{k=0..n} Sum_{j=0..n} binomial(floor((n + k + j)/3), k)*binomial(k, floor((n + k + j)/3)).
G.f.: 1 - x*(-3 - 2*x + 2*x^2)/((1 + x)*(x - 1)^2). - R. J. Mathar, Oct 25 2011
E.g.f.: ((4 + 3*x)*cosh(x) + 3*(1 + x)*sinh(x) - 2)/2. - Stefano Spezia, Feb 20 2023
MATHEMATICA
Join[{1, 3}, LinearRecurrence[{1, 1, -1}, {5, 6, 8}, 100]] (* Vladimir Joseph Stephan Orlovsky, Jan 31 2012 *)
CROSSREFS
Sequence in context: A184675 A336410 A121506 * A186324 A101358 A276210
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Nov 13 2005
STATUS
approved

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Last modified February 21 20:41 EST 2024. Contains 370237 sequences. (Running on oeis4.)