OFFSET
0,2
COMMENTS
This sequence has first six terms same as Cake numbers (A000125) after that it is different. The difference can be explained by duplicated tetrahedral numbers.
LINKS
Index entries for linear recurrences with constant coefficients, signature (1,3,-3,-3,3,1,-1).
FORMULA
a(n) = {(14*n^3+15*n^2+49*n+111)-(3*n^2-15*n+15)(-1)^n}/96.
G.f.: ( 1+x-x^2+x^3+4*x^4+2*x^5-x^6 ) / ( (1+x)^3*(x-1)^4 ). - R. J. Mathar, Jan 19 2012
a(0)=1, a(1)=2, a(2)=4, a(3)=8, a(4)=15, a(5)=26, a(6)=41, a(n)=a(n-1)+ 3*a(n-2)-3*a(n-3)-3*a(n-4)+3*a(n-5)+a(n-6)-a(n-7). - Harvey P. Dale, Apr 17 2012
EXAMPLE
a(7) = ((14*7^3+15*7^2+49*7+111)-(3*7^2-15*7+15)(-1)^7)/96 = 63.
MAPLE
seq(binomial(n, 3)+binomial(n, 2)+binomial(n, 1)+binomial(n, 0)- binomial(floor(n/2), 3) , n=0..29);
MATHEMATICA
Table[Total[Table[Binomial[n, i], {i, 0, 3}]]-Binomial[Floor[n/2], 3], {n, 0, 60}] (* or *) LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {1, 2, 4, 8, 15, 26, 41}, 60] (* Harvey P. Dale, Apr 17 2012 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Darshana Patel, Jan 16 2012
EXTENSIONS
More terms from Harvey P. Dale, Apr 17 2012
STATUS
approved