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 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. 0
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 22 16:46 EDT 2023. Contains 365531 sequences. (Running on oeis4.)