A265038 Partial sums of A009927.
1, 13, 63, 183, 401, 745, 1291, 2019, 2921, 4133, 5659, 7443, 9597, 12149, 15103, 18535, 22389, 26729, 31727, 37231, 43233, 50001, 57443, 65467, 74281, 83853, 94187, 105419, 117397, 130221, 144159, 158927, 174517, 191329, 209175, 227927, 247889, 268969, 291171, 314691
Offset: 0
Keywords
Links
- V. A. Blatov, A. P. Shevchenko, D. M. Proserpio, Applied Topological Analysis of Crystal Structures with the Program Package ToposPro, Cryst. Growth Des. 2014, 14, 3576-3586. See Table I.
Crossrefs
Cf. A009927.
Formula
Empirical: Sum_{k=0..n} [(1903/72) + (3/8)*(-1)^k +19*KroneckerDelta[k,0] - 8*KroneckerDelta[k,1] - 12*KroneckerDelta[k,2] + ((k+1)/12)*(187*k-273) - (32*sqrt(3)/27)*((13/2)*cos((4k+1)*Pi/6) + sin(2k*Pi/3)) - (3*sqrt(26)/2)*(-1)^n*cos(k*Pi/2 + arctan(1/5)) - (3/4)*i^k*(1+(-1)^k)*(k+2)].- G. C. Greubel, Dec 18 2015
Empirical g.f.: (1 +12*x +51*x^2 +130*x^3 +243*x^4 +350*x^5 +450*x^6 +418*x^7 +327*x^8 +182*x^9 +51*x^10 +16*x^11 -7*x^12 +8*x^13 +12*x^14) / ((1 -x)^4*(1 +x)*(1 +x^2)^2*(1 +x +x^2)^2). - Colin Barker, Dec 19 2015
Comments