A114119 Row sums of triangle A114118.

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

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

Table of n, a(n) for n=0..69.

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

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

Cf. A007494, A049636, A045506.

Sequence in context: A184675 A336410 A121506 * A186324 A101358 A276210

Adjacent sequences: A114116 A114117 A114118 * A114120 A114121 A114122

Keyword

easy,nonn

Author

Paul Barry, Nov 13 2005

Status

approved