OFFSET
1,2
COMMENTS
The exponents in the q-series for A204220 are the squares of the numbers of this sequence.
The product of any two terms belongs to the sequence and therefore also a(n)^2, a(n)^3, a(n)^4, etc. - Bruno Berselli, Nov 28 2012
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..5000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).
FORMULA
G.f.: x * (1 + 3*x + 7*x^2 + 3*x^3 + x^4) / ((1-x) * (1-x^4)).
a(n) = -a(1-n), a(n) = 15 + a(n-4), a(n) = floor(15 * n / 4) - ((n + 1) mod 4) for all n in Z.
a(n) = (30*n+10*i^(n*(n+1))-3*(-1)^n+1)/8 -2, where i=sqrt(-1). - Bruno Berselli, Nov 28 2012
a(n) = a(n-1) + a(n-4) - a(n-5) for n>5. - Wesley Ivan Hurt, Jun 07 2016
E.g.f.: (4 - 5*(sin(x) - cos(x)) + 3*(5*x - 2)*sinh(x) + 3*(5*x - 3)*cosh(x))/4. - Ilya Gutkovskiy, Jun 07 2016
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(2*(sqrt(5)+5))*Pi/15. - Amiram Eldar, Dec 30 2021
EXAMPLE
G.f. = x + 4*x^2 + 11*x^3 + 14*x^4 + 16*x^5 + 19*x^6 + 26*x^7 + 29*x^8 + 31*x^9 + ...
MAPLE
A204542:=n->floor(15 * n / 4) - ((n + 1) mod 4): seq(A204542(n), n=1..100); # Wesley Ivan Hurt, Jun 07 2016
MATHEMATICA
Select[Range[250], MemberQ[{1, 4, 11, 14}, Mod[#, 15]]&] (* or *) LinearRecurrence[{1, 0, 0, 1, -1}, {1, 4, 11, 14, 16}, 60] (* Harvey P. Dale, Apr 15 2015 *)
PROG
(PARI) {a(n) = (n * 15) \ 4 - (n + 1) % 4};
(PARI) {a(n) = if( n<1, -a(1-n), polcoeff( x * (1 + 3*x + 7*x^2 + 3*x^3 + x^4) / ((1-x) * (1-x^4)) + x * O(x^n), n))};
(Magma) [n : n in [0..100] | n mod 15 in [1, 4, 11, 14]]; // Wesley Ivan Hurt, Jun 07 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michael Somos, Jan 16 2012
STATUS
approved