OFFSET
0,3
COMMENTS
An interleaved sequence of pyramidal and polygonal numbers: a(2n)= A006527(n+1), a(2n+1)=A000330(n+1) - Paul Barry, Mar 17 2003
a(n) is also the number of solutions to the equation XOR(x1, x2, ..., xn) = 0 such that each xi is a 2-bit binary number and xi >= xj for i >= j. For example, a(2) = 4 since (x1, x2) = { (00, 00), (01, 01), (10, 10), (11, 11) }. - Ramasamy Chandramouli, Jan 17 2009
These are also the "spreading numbers" alpha_4(n). See Babcock et al. for precise definition.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
B. Babcock and A. van Tuyl, Revisiting the spreading and covering numbers, arXiv preprint arXiv:1109.5847 [math.AC], 2011-2013.
John Machacek, Unique maximum independent sets in graphs on monomials of a fixed degree, arXiv:2010.11112 [math.CO], 2020.
Index entries for linear recurrences with constant coefficients, signature (2,1,-4,1,2,-1).
FORMULA
G.f.: (x^2-x+1)/((1-x^2)^2*(1-x)^2).
a(n) = (n+2)*(2*n^2 + 8*n + 15 + 9*(-1)^n)/48. - Vaclav Kotesovec, Mar 16 2014
MATHEMATICA
Table[(n+2)*(2*n^2 + 8*n + 15 + 9*(-1)^n)/48, {n, 0, 20}] (* Vaclav Kotesovec, Mar 16 2014 *)
PROG
(PARI) for(n=0, 30, print1((n+2)*(2*n^2 + 8*n + 15 + 9*(-1)^n)/48, ", ")) \\ G. C. Greubel, May 31 2018
(Magma) [(n+2)*(2*n^2 + 8*n + 15 + 9*(-1)^n)/48: n in [0..30]]; // G. C. Greubel, May 31 2018
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Mar 05 2000
STATUS
approved