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

Author

N. J. A. Sloane, Dec 15 2015

Keywords

• nonn

Comments

Needs a b-file (not based on any conjectures, of course). - N. J. A. Sloane, Dec 18 2015

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