A204555 The number of subsets of the numbers {1,2,3...,n} consisting of at most 3 elements and at most two of those are even.

1, 2, 4, 8, 15, 26, 41, 63, 89, 126, 166, 222, 279, 358, 435, 541, 641, 778, 904, 1076, 1231, 1442, 1629, 1883, 2105, 2406, 2666, 3018, 3319, 3726, 4071, 4537, 4929, 5458, 5900, 6496, 6991, 7658, 8209, 8951, 9561, 10382, 11054, 11958, 12695, 13686, 14491

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

Table of n, a(n) for n=0..46.

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

Cf. A000125, A058187.

Sequence in context: A324740 A262146 A089140 * A000125 A129961 A133551

Adjacent sequences: A204552 A204553 A204554 * A204556 A204557 A204558

Keyword

nonn,easy

Author

Darshana Patel, Jan 16 2012

Extensions

More terms from Harvey P. Dale, Apr 17 2012

Status

approved