OFFSET
0,2
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..2500
Kyu-Hwan Lee, Se-jin Oh, Catalan triangle numbers and binomial coefficients, arXiv:1601.06685 [math.CO], 2016.
Index entries for linear recurrences with constant coefficients, signature (2,0,-1,-1,0,2,-1).
FORMULA
G.f.: (1 + x + 2*x^2 + x^3) / ((1 - x)^2 * (1 - x^2) * (1 - x^3)).
a(n) - 2*a(n+1) + 2*a(n+3) - a(n+4) = -1 if n == 0 (mod 3) else -2 for all n in Z.
a(n) = -A254874(-4-n) for all n in Z.
EXAMPLE
G.f. = 1 + 3*x + 8*x^2 + 16*x^3 + 28*x^4 + 45*x^5 + 68*x^6 + 97*x^7 + ...
MATHEMATICA
a[ n_] := Quotient[ 10 n^3 + 57 n^2 + 102 n + 72, 72];
Table[Floor[(10n^3+57n^2+102n+72)/72], {n, 0, 60}] (* or *) LinearRecurrence[ {2, 0, -1, -1, 0, 2, -1}, {1, 3, 8, 16, 28, 45, 68}, 60] (* Harvey P. Dale, Jan 07 2017 *)
PROG
(PARI) {a(n) = (10*n^3 + 57*n^2 + 102*n + 72) \ 72};
(PARI) {a(n) = polcoeff( (-1)^(n<0) * (if( n<0, n = -4 - n; x, x^2) + 1 + x + x^2 + x^3) / ((1 - x)^2 * (1 - x^2) * (1 - x^ 3)) + x * O(x^n), n)};
(Magma) [Floor((10*n^3 +57*n^2 +102*n +72)/72): n in [0..30]]; // G. C. Greubel, Aug 03 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael Somos, Feb 09 2015
STATUS
approved